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arpita biswas

· started a discussion

· 1 Months ago

Arpita (Question: 535700.0 )

Not clear

Question:
Shortest median of right angle is 60 cm, and perimeter is 260 cm. find area of \(\Delta\)ABC = ?


Options:
A) 1300
B) 2600
C) 1600
D) 1200
Solution:
The shortest median in right angle triangle is always drawn to hypotenuse 

and the median on the hypotenuse of a right triangle equals to one-half 

the hypotenuse.


\(b^2 + h^2 = 120^2\)=\(14400 cm^2\)-------------(1)

perimeter \(( P)\) = 260 cm

P = b + h + 120 

(\(( b + h )^2 =( 140 )^2\)----------------(2)


By subtracting eq(1) from eq(2)
\(( b + h)^2 - ( b^2+ h^2)=140^2-120^2\)

 \(b^2+ h^2 +2bh - b^2 -h^2 =5200\)

 2bh=5200

\(bh= 2600 cm^2\)

 \(\therefore\)\(Area=\frac{1}{2}\times 2600 =1300cm^2 \)

Alternate solution:

 

If BM is a median in right angle triangle 

BM=60 cm

AM=MC=BM=BC

AC=2\(\times\)BM

AC=120 cm

AB+BC+CA=260cm

AB+BC+120=260

AB+BC=140cm

Taking both side square 

(AB+BC)2=1402

AB+BC+2\(\times\)AB\(\times\)BC=19600 cm

AB\(\times\)BC=2600 cm

Area of triangle = \(\cfrac{1}{2}\times base\times height \)

                    =    \(\cfrac{1}{2}\times BC\times AB =\cfrac{1}{2}\times2600 \)

                  = 1300 cm2

Knowledge Expert

· commented

· 1 Months ago

Dear student
We have updated the question
and solution, please solve again.

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