Question

if the difference between the sides of a right angled triangle is 3cm and its area is 54cm2.find its perimeter

Answer 1

Let the two sides be x and x + 3
Area = 54 cm^2
1/2 (x)(x+3) = 54

x² + 3x = 108

x² + 3x - 108 = 0

(x+12)(x-9) = 0

x = 9

Sides are 9 cm and 12 cm

Hypotenuse = $\sqrt{9^2 + 12^2}$
                
                    = $\sqrt{81 + 144}$

                    = $\sqrt{225}$
  
                   = 15 cm

Perimeter of triangle = 9 + 12 + 15 = 36  cm