Question

Find the perimeter of an isosceles right triangle having an area of 5000 metre square

Answer 1

Hey Friend,


Since the triangle is isosceles triangle,
Let the perpendicular and the base be 'x' cm.

According to given,
Area = 5000 m^2
1/2 x h x b = 5000 m^2
x^2 = 10000 m^2
x = 10 m 

Therefore, the sides are 10 cm.

Now, Applying Pythagoras theorem,
hypotenuse^2 = height^2 + base^2
hypotenuse^2 = 10^2 + 10^2
hypotenuse^2 = 100 + 100
hypotenuse =  $\sqrt{200}$
hypotenuse = 10 $\sqrt{2}$
hypotenuse = 10 x 1.414
hypotenuse = 14.14 m

Therefore, the hypotenuse is 14.14 m

Perimeter = 2x + hypotenuse
Perimeter = 20 + 14.14
Perimeter = 34.14 m

Therefore, the perimeter of triangle is 34.14 m.

Hope it helps!