Question

15. The sides of a right-angled triangle containing the
right angle are 5x cm and (3x - 1) cm. If the area of
the triangle be 60 cm", calculate the lengths of the
sides of the triangle.
(ICSE)
2​

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. x = 3 (or) x = -3/8. ... Therefore the sides of the triangle are 8cm,15cm, and 17cm.

Answer 2

Answer:

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!