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.