Triangle Based Questions For Aptitude Exams for DU JAT and IPM 2027

Overview: Master DU Triangle Based Questions for Aptitude Exam with this comprehensive guide covering essential triangle properties, formulas, shortcut techniques, and exam-oriented concepts. Practice 35 solved MCQs with detailed explanations to strengthen your problem-solving speed and accuracy for DU and other competitive aptitude exams in 2027.

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Important accuracy note: DU JAT has been discontinued since 2022. Admission to Delhi University's BBA (FIA), BMS and BBE programmes is now based on CUET-UG, conducted by the NTA. 

If you searched for "DU JAT triangle questions," every concept and practice set below applies equally to CUET (BBA) quantitative ability and to IPMAT.

Quick Facts: Triangles in the DU / CUET (BBA) Aptitude Exam

Parameter	Details
Parent topic	Geometry (Quantitative Ability)
Exams where it appears	CUET (BBA) for DU, IPMAT Indore, IPMAT Rohtak, JIPMAT, NPAT, SET
Current DU admission route	CUET-UG (NTA) → DU CSAS counselling
IPMAT Indore quant structure	30 QA-MCQ + 15 QA-SA (45 quant) + 45 Verbal = 90 total
Typical difficulty	Easy to Moderate
Most-tested concepts	Pythagoras' theorem, area, similarity & congruence, triangle inequality
Ideal time per question	45–60 seconds
Must-memorise	Pythagorean triplets, 30-60-90 & 45-45-90 ratios, Heron's formula

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Key Highlights

• The triangle inequality (any two sides sum to more than the third) filters out impossible options instantly.

• Memorising Pythagorean triplets saves 20–30 seconds per right-triangle question.

• The two special right triangles — 45-45-90 and 30-60-90 — cover a large share of exam questions.

• Similarity and congruence rules (SSS, SAS, AAS, RHS, AA) are frequently tested through figure-based questions.

• Accuracy beats coverage: attempt the DU triangle-based questions for the aptitude exam that you are confident about first, since cut-offs are never 100%.

Also Read: Important IPMAT Arithmetic Questions to Practice Now 

5 Solved DU Triangle-Based Questions for Aptitude Exam 2027

Example 1: The area of a triangle is 615 cm². If one side is 123 cm, find the length of the perpendicular dropped on that side from the opposite vertex.

1. 10 cm
2. 50 cm
3. 0.16 cm
4. 0.2 cm

Solution: Area = ½ × base × height ⟹ 615 = ½ × 123 × H ⟹ H = 10 cm. Answer: A.

Example 2: Two sides of an isosceles triangle are 12.5 cm each and the third side is 20 cm. Find the area.

12. 25 cm²
13. 75 cm²
14. 12 cm²
15. 10 cm²

Solution: s = (12.5 + 12.5 + 20) / 2 = 22.5. Using Heron's formula, Area = √[22.5 × 10 × 10 × 2.5] = 75 cm². Answer: B.

Example 3: One side of a triangle is 3 cm and the perimeter is 8 cm. If the area is maximum, the other two sides are:

1. (3, 3)
2. (7, 5)
3. (2/3, 2)
4. (5/2, 5/2)

Solution: With a + b + 3 = 8, we get a + b = 5. Area = ½ × a × b × sin θ; the angle is fixed, so area is maximum when the product ab is maximum. For a fixed sum, the product is largest when a = b, giving a = b = 5/2. Answer: D.

Example 4: An obtuse triangle has sides 8 cm, 15 cm and an unknown integer third side. How many such triangles exist?

1. 20
2. 10
3. 13
4. 15

Solution: Use the obtuse condition (c² > a² + b², c = longest side) with the triangle inequality.
Case 1 — x is the longest side: 17 < x < 23 gives x = 18, 19, 20, 21, 22 → 5 values.
Case 2 — 15 is the longest side: 7 < x < 12.56 gives x = 8, 9, 10, 11, 12 → 5 values.
Total = 5 + 5 = 10. Answer: B.

Example 5: A circle is inscribed in an equilateral triangle of side 24 cm, touching all its sides. Find the area of the region inside the triangle but outside the circle.

1. 144√3 − 48π cm²
2. 122√3 − 36π cm²
3. 147√3 − 36π cm²
4. 130√3 − 47π cm²

Solution: Height h = (√3/2) × 24 = 12√3. Inradius r = h/3 = 4√3. Area of triangle = (√3/4) × 24² = 144√3. Area of circle = πr² = π(4√3)² = 48π. Remaining area = 144√3 − 48π. Answer: A.

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Triangle Practice Questions for the DU / CUET (BBA) Aptitude Exam

Attempt these under timed conditions — aim for under a minute each. Answers are listed at the end of the set so you can practise a full block before checking.

1. The angles of a triangle are in the ratio 2 : 3 : 4. The largest angle is:

1. 40°
2. 60°
3. 80°
4. 90°

2. Two sides of a triangle are 7 cm and 10 cm. Which of the following cannot be the length of the third side?

1.  4 cm
2. 8 cm
3. 15 cm
4. 17 cm

3. The area of an equilateral triangle of side 10 cm is:

1. 25√3 cm²
2. 50√3 cm²
3. 100√3 cm²
4. 25 cm²

4. In a right triangle, the two legs are 9 cm and 12 cm. The hypotenuse is:

1. 13 cm
2. 15 cm
3. 21 cm
4. 16 cm

5. An exterior angle of a triangle is 110°, and one remote interior angle is 45°. The other remote interior angle is:

1.  55°
2. 65°
3. 70°
4. 45°

6. The sides of a triangle are 13 cm, 14 cm and 15 cm. Its area is:

1.  84 cm²
2. 91 cm²
3. 42 cm²
4. 168 cm²

7. In a 30-60-90 triangle, the side opposite the 30° angle is 5 cm. The hypotenuse is:

1.  5√3 cm
2. 10 cm
3. 5√2 cm
4. 15 cm

8. The perimeter of an equilateral triangle is 36 cm. Its height is:

1. 6√3 cm
2. 12√3 cm
3. 6 cm
4. 18 cm

9. If two angles of a triangle are 50° and 60°, the triangle is:

1. Right-angled
2. Obtuse
3. Acute
4. Equilateral

10. The base of an isosceles triangle is 16 cm and each equal side is 10 cm. Its area is:

1. 48 cm²
2. 96 cm²
3. 80 cm²
4. 60 cm²

11. In △ABC, ∠A = 90°, AB = 8, AC = 6. The length of the altitude from A to BC is:

1. 4.8
2. 5
3. 3.6
4. 4

12. The sides of a right triangle are in the ratio 3 : 4 : 5 and its perimeter is 60 cm. The area is:

1. 120 cm²
2. 150 cm²
3. 96 cm²
4. 60 cm²

13. Which set of sides forms a right triangle?

1.  6, 8, 11
2. 5, 12, 13
3. 7, 8, 9
4. 4, 5, 6

14. The medians of a triangle intersect at a point that divides each median in the ratio:

1.  1: 1
2. 1: 2
3. 2: 1
4. 3: 1

15. In a 45-45-90 triangle, each equal side is 7 cm. The hypotenuse is:

1. 7 cm
2. 7√2 cm
3. 14 cm
4. 7√3 cm

16. The area of a triangle with base 18 cm and height 9 cm is:

1. 81 cm²
2. 162 cm²
3. 27 cm²
4. 90 cm²

17. If the angles of a triangle are (x + 10)°, (2x)° and (3x − 10)°, then x equals:

1. 25
2. 30
3. 35
4. 40

18. Two similar triangles have areas in the ratio 9 : 16. The ratio of their corresponding sides is:

1. 3 : 4
2. 9 : 16
3. 81 : 256
4. 4 : 3

19. The hypotenuse of a right triangle is 25 cm and one leg is 7 cm. The other leg is:

1. 18 cm
2. 24 cm
3. 20 cm
4. 22 cm

20. An equilateral triangle and a square have equal perimeters. If the square's side is 6 cm, the triangle's side is:

1.  6 cm
2. 8 cm
3. 9 cm
4. 12 cm

21. In a triangle, the largest angle is 100°. The triangle is:

1. Acute
2. Right
3. Obtuse
4. Equilateral

22. The inradius of an equilateral triangle of side 12 cm is:

1.  2√3 cm
2. 4√3 cm
3. 2 cm
4. 6 cm

23. The circumradius of an equilateral triangle of side 6 cm is:

1.  2√3 cm
2. √3 cm
3. 3 cm
4. 6 cm

24. A triangle has sides 9, 12 and 15. The length of the altitude to the longest side is:

1.  6.4
2. 7.2
3. 5.4
4. 8

25. If one angle of an isosceles triangle is 100°, the two equal base angles are each:

1. 30°
2. 40°
3. 45
4. 50°

26. The ratio of the area of an equilateral triangle to a square built on the same side length is:

1. √3 : 4
2. 4 : √3
3. 1 : 2
4. √3 : 2

27. In △ABC, DE ∥ BC with D on AB and E on AC. If AD = 3, DB = 6 and AE = 4, then EC is:

1.  6
2. 8
3. 12
4. 2

28. The sides of a triangle are 6 cm, 8 cm and 10 cm. Its area is:

1. 24 cm²
2. 30 cm²
3. 48 cm²
4. 40 cm²

29. How many degrees are there in each angle of an equilateral triangle?

1. 45°
2. 60°
3. 90°
4. 30°

30. The perimeter of a right triangle is 24 cm and its hypotenuse is 10 cm. The area is:

1. 20 cm²
2. 24 cm²
3. 30 cm²
4. 12 cm²

Answer Key (Questions 1–30)

Q	Ans	Q	Ans	Q	Ans
1	3	11	1	21	3
2	4	12	2	22	1
3	1	13	2	23	1
4	2	14	3	24	2
5	2	15	2	25	2
6	1	16	1	26	1
7	2	17	2	27	2
8	1	18	1	28	1
9	3	19	2	29	2
10	1	20	3	30	2

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Why DU Triangle-Based Questions for the Aptitude Exam Matter?

Geometry appears every single year in the quant section, and triangles are its backbone. Lines, angles and triangles together account for a meaningful chunk of geometry questions in CUET (BBA), IPMAT Indore and IPMAT Rohtak papers.

Because DU admissions now run through CUET, DU triangle-based questions for aptitude exam practice are really CUET (BBA) quant practice; the syllabus overlap is almost total.

The good news: this is a "learn once, score forever" topic. Once your triangle properties are solid, the questions become fast, predictable and high-accuracy.

Common Mistakes in DU Triangle-Based Questions for Aptitude Exam 2027

• Skipping the triangle inequality check. Most "how many triangles are possible" problems are solved by the inequality alone.

• Confusing similarity with congruence. Area ratio = (side ratio)², not the side ratio itself.

• Misapplying the 30-60-90 ratio. The ratio 1 : √3 : 2 maps to angles 30 : 60 : 90 — match each side to its opposite angle.

• Forgetting Pythagorean triplets. Recognising 8-15-17 instantly avoids a full calculation.

• Over-attempting. Cut-offs are never 100% — bank high-accuracy questions first.

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Expert Tip to Master DU Triangle-Based Questions for Aptitude Exam 2027

Do not attempt to solve every question — the cut-off is never 100%. Pick the low-hanging fruit: attempt the DU triangle-based questions for the aptitude exam you are confident about, and prioritise accuracy over volume.

In IPMAT Indore's QA-SA section, there is no negative marking, so enter an answer for every short-answer question — even an educated estimate.

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• How to Prepare for Geometry in IPMAT
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Summary

Triangles reward preparation more predictably than almost any other quant sub-topic.

For DU triangle based questions for aptitude exam success — and for CUET (BBA), IPMAT, JIPMAT and NPAT — lock in the triangle inequality, the Pythagorean theorem and its triplets, the 45-45-90 and 30-60-90 special triangles, the similarity and congruence rules, and the standard area formulas.

Practise the 35 solved questions above until each type feels automatic, and triangle questions become guaranteed marks.