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jyoti

· started a discussion

· 1 Months ago

area of equilateral triangle (Question: 108611.0 )

area of equilateral triangle (formula)

Question:
Manik Singhaniya stands on the tip of an equilateral triangle whose area is   \(36 \sqrt[]{3}\) m2. He goes around the three sides and returns to the same tip. Then he goes North and covers as much distance as before. He turns right and reaches point P which is parallel to tip of equilateral triangle. What is the shortest distance from original to starting point?
Options:
A) 36 m 
B) 144 m
C) 72 m
D) 2\(\sqrt[]{333}\) m
E) Can’t be determined
Solution:
Ans: (d) The movements of Manik Singhaniya are as shown in Fig, i.e, A to B, B to C, C to, A, A to Q and Q to P.


A = Starting point,     P = End point 

Given, Area of equilateral triangle ABC = 36 \(\sqrt[]{3}\) m2

∴\(\cfrac{\sqrt[]{3}}{4}\) (side)2 = 36 \(\sqrt[]{3}\)

or, side = 6 × 2 = 12

Therefore, Manik Singhaniya's shortest distance from the starting point A

= \(\sqrt[]{1296+36}=2\sqrt[]{333}\) m

Knowledge Expert

· commented

· 1 Months ago

√3 / 4 (side)^2.....
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