Find the length of the hypotenuses of an isosceles right –angled triangle whose area is 200 cm 2 . Also, find its perimeter. [Given: √2 = 1.41.]

Question

Philoid · Accepted Answer

Given: Area = 200 cm

Let the equal sides be a.

We know that,

Area of a triangle = 1/2 × Base × Height

⇒ 200 = 1/2 × a × a

⇒ 200 = 1/2 × a²

⇒ a² = 200 × 2

⇒ a² = 400

⇒ a = 20 cm

Now,

Base² + Perpendicular² = Hypotenuse²

⇒ 20² + 20² = Hypotenuse²

⇒ Hypotenuse² = 400 + 400

⇒ Hypotenuse² = 800 cm²

⇒ Hypotenuse= 20√2 cm

⇒ Hypotenuse= 28.2 cm

Now,

Perimeter of triangle = 20 + 20 + 28.2 cm

= 68.2 cm