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Find the length of the hypotenuse of an isosceles right-angled triangle whose area is 200 cm2 . Also, find its perimeter

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In a right isosceles triangle, base = height = a

Therefore,

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

\(\Rightarrow \frac{1}{2}a^2=200\)

\(\Rightarrow \) a2 = 400

or, a = \(\sqrt{400}\) = 20 cm

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

Therefore, c = \(\sqrt{a^2+a^2}\)

\(\sqrt{2a^2}\)

\(a\sqrt{2}\)

= 20 x 1.41

= 28.2 cm

Perimeter of the triangle = a + a + c

= 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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