If the perimeter of an isosceles right triangle is (16√2 + 16) cm, then the area of the triangle is :
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Correct answer: B
Explanation
The correct answer is Option 2 i.e. 64 sq. cm.
The perimeter isosceles right triangle is a(2 + √2) (where a is the common side)
⇒ a(2 + √2) = (16√2 + 16)
⇒√2 a(√2 + 1) = 16(√2 + 1)
⇒√2a = 16
⇒ a = 16/√2
Now,
Area of triangle = 1/2 × a × a
⇒ 1/2 × 16/√2 × 16/√2
⇒ 256/4
⇒ 64