Question

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

Answer 1

Solution -

Area of a triangle = 1/2 * b * h

As it is an isosceles right triangle, b = h 

Therefore, Area = 1/2 * b * b = 1/2 * b^2

200 = 1/2 * b^2

b^2 = 400

b = 20 cm

Therefore, b = h = 20 cm

Perimeter of a triangle = b + h + sqrt (b^2 + h^2)
                                   
                                       = 20 + 20 + sqrt ((20)^2 + (20)^2)
      
                                       = 40 + sqrt(400 + 400)
                        
                                       = 40 + sqrt(800)
          
                                       = 40 + 20 sqrt 2 cm
                                 
                                       = 40 + 20 * 1.414     (as sqrt 2 = 1.414)
                   
                                       = 68.28 cm

Answer - Perimeter of an isosceles right triangle = 68.28 cm

Answer 2

Area of an isosceles triangle = 1/2*base*height
Here it is a right angled triangle,
then perpendicular = base = x
So, area = 1/2*x*x
x² = 400
x = 20 cm
So, Perpendicular = base = 20 cm
By Pythagoras Theorem
H² = P² + B²
H² = 20² + 20²
H² = 400 + 400
H² = 800
H = 20√2
Perimeter = 20 + 20 + 20√2
⇒ 40 + 20√2
= 68.28 cm
Answer.