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Question

Find the length of the hypotenuse of an isosceles right-angled triangle whose area is 200 cm2. Also, find its perimeter. [Given: 2 = 1.41]

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Solution

In a right isosceles triangle, base=height=a

Therefore,
Area of the triangle = 12×base×height=12×a×a=12a2

Further, given that area of isosceles right triangle = 200 cm2

12a2=200a2=400or, a=400 =20 cm

In an isosceles right triangle, two sides are equal ('a') and the third side is the hypotenuse, i.e. 'c'

Therefore, c = a2+a2

= 2a2= a2= 20×1.41= 28.2 cm

Perimeter of the triangle = a+a+c
ā€‹ =20+20+28.2

= 68.2 cm

The length of the hypotenuse is 28.2 cm and the perimeter of the triangle is 68.2 cm.

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