Answer:

Step-by-step explanation:

Find the perimeter of an isosceles right triangle whose area is 200 cm^2.

since , we know that in isosceles triangle two sides are always equal. but here given that the isosceles triangle is right triangle . if the triangle is isosceles right triangle then its base and height will be equal.

why hypotenuse will not be equal either to height or base of isosceles right triangle ?

its because , according pythagoras theorem

if the triangle is right (90°) then the length of hypotenuse of that triangle will always be greater than the base and the height of that triangle.

let b be the hypotenuse and ( a , a ) be the base and height of isosceles right triangle.

from ∆ ABC

area of isosceles right triangle=200cm^2

( 1 / 2 ) × base × height = 200

( 1 × a × a ) / 2 = 200

a^2 = 400 => a = √400 => a = 20 cm

now in ∆ ABC ,

by Pythagoras theorem , we get

(AC)^2 = ( BC )^2 + ( AB )^2

b^2 = ( 20 )^2 + ( 20 )^2

b^2 = 400 + 400 = 800

b = √800 => 28.2 cm ( approx. )

since , we know that perimeter of triangle

= sum of all the sides of triangle.

therefore, perimeter of isosceles right triangle

= a + a + b = 20 + 20 + 28.2 = 68.2 cm

Your Answer : 68.2 cm

THEREFORE, Perimeter of an isosceles right triangle whose area is 200 cm= 68.2 cm