Question

the length of sides formong a right angled triangle is 5x cm and 3x-4 areas of the triangle is 60 cm square. find the hypotenuse​

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 = \sqrt{289}

= 17.

Therefore the hypotenuse = 17cm.

Therefore the sides of the triangle are 8cm,15cm, and 17cm.