Question

The sides of a right angled triangle containing the right angle are 5x cm and (3x-1) cm.if it's area is 60 cm^2 , find its perimeter

Answer 1

Given that sides of a right-angled triangle are 5x and (3x - 1)cm.

Given that Area of the triangle = 60cm^2.

We know that Area of the triangle = 1/2 * b * h

                              60 = 1/2 * 5x * (3x - 1)

                             5x(3x - 1) = 60 * 2

                             5x(3x - 1) = 120

                             x(3x - 1) = 120/5

                              3x^2 - x = 24

                              3x^2 - x - 24 = 0

                              3x^2 + 8x - 9x - 24 = 0

                              x(3x + 8) - 3(3x + 8)

                              (x - 3)(3x + 8)

                              x = 3 (or) x = -3/8.


x value should not be -ve.Therefore the value of x = 3.

Therefore the sides of a right-angled triangle = 

5x = 5 * 3 = 15cm

(3x - 1) = (3 * 3 - 1)

           = 9 - 1

           = 8cm

 
By Pythagoras theorem, we know that 

h^2 = 15^2 + 8^2

       = 225 + 64

       = 289

h = 

   = 17.


Therefore the hypotenuse = 17cm.

Therefore the sides of the triangle are 8cm,15cm, and 17cm.
Hope this helps!