Question

The sides of a right angled triangle containing the right angle are [ 5x ]cm & ( 3x-1 ) cm. if its area is 60 cm square, find its perimeter of triangle

Answer 1

Answer:

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.