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Question

# The perimeter of an isosceles right angled triangle is 2p. Its area is

A
p2(2+2)
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B
p2(22)
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C
p2(322)
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D
p2(3+22)
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Solution

## The correct option is D p2(3+2√2)The ratio of the sides of an isosceles right triangle is1:1:√2 .By the Pythogoras Theorem,The perimeter (P) is,P=1x+1x+(√2)x =(2+√2)x =2p x=2p(2+√2) Here x is the scale factor and it is also the length of each of the two identical sides 1x.Therefore,The area is,A=12×b×h =12×(1x)×(1x) =x22=⎛⎝(2p(2+√2))22⎞⎠ =2p2(2+√2) =2p2(4+4√2+2) =2p2(6+4√2) =p2(3+2√2)

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