Question

The length of sides of a right angled triangle forming the right angle are 5x cm and (3x – 1) cm. If the

area of the triangle is 60 cm2

, find its all sides.​

Answer 1

Step-by-step explanation:

1/2 bh

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

1/2 (15x^2 -5x ) = 60

15x^2 - 5x = 120

15x^2 -5x - 120 = 0

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 = -8/3

since length cannot be -ve

x = 3

so the sides of the triangle are

5(3) and 3(3) - 1 = 15 and 8

By Pythogorean prop

8^2 + 15^2 = hypotenuse ^2

(sum of the squares on the two non - hypotenuse sides is equal to the square on the hypotenuse )

64 + 225 = 289

hypotenuse sqr = 289

hypotenuse = Root of 289

Hyp - 17