Find the length of the hypotenuse of an isosceles right-angled triangl

1.	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]
Answer» Let two sides of an isosceles right-angled triangle are of measure “a”. Area of triangle = 200 cm². (given) 200 = 1/2(a²) => a = 20 cm Now, Hypotenuse = √(a²+a²) = √(2a²) = √2 a = 20 √2 = 20 x 1.414 = 28.28 => Hypotenuse is 28.28 cm Perimeter of triangle = Sum of all the sides = 2a + Hypotenuse = 40 + 28.28 = 68.28 => Perimeter of triangle is 68.28 cm.

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]

Answer»

Let two sides of an isosceles right-angled triangle are of measure “a”.

Area of triangle = 200 cm². (given)

200 = 1/2(a²)

=> a = 20 cm

Now,

Hypotenuse = √(a²+a²) = √(2a²) = √2 a

= 20 √2

= 20 x 1.414

= 28.28

=> Hypotenuse is 28.28 cm

Perimeter of triangle = Sum of all the sides = 2a + Hypotenuse

= 40 + 28.28

= 68.28

=> Perimeter of triangle is 68.28 cm.