Question

In an isosceles right-angled triangle, the square of the hypotenuse is 200 cm square. Find the length of each side of the triangle.​

Answer 1

In an isosceles right angled triangle, the two sides on the right angle are equal

Let the equal side be a

Hence, hypotenuse of the isosceles right angled triangle of side a

$\sf \red{ \implies} \sqrt{ {a}^{2} + {a}^{2} } = \sqrt{2a}$

In the isosceles right triangle, the base and

height = a

${ \tt{ Hence, \: area \: of \: the triangle = \frac{1}{2} \times base \times }}$

height=

$\sf{ \tt{ \frac{1}{2} \times a \times a = 200 \: SQ \: cm.}} \\ \sf{ \tt{ \implies {a}^{2} = 400 }} \\ \sf{ \tt{ \implies a = 20cm.}} \\ \sf{ \tt{and \: the \: hypotenuse = \sqrt{2a} = 20 { \sqrt{ 2}cm. }}}$