Question

The hypotenuse of a right-angled triangle is 5 m. If the smaller side is doubled and the longer side is tripled, the new hypotenuse is `6sqrt5` m. Find all the sides of the triangle.

Answer 1

Let the smaller side of the right-angled triangle be x m and the longer side be y m.

Given:

Original hypotenuse = 5 m

x² + y² = 25     ...(1)

When the smaller side is doubled and the longer side is tripled, new hypotenuse `= 6sqrt5` m

`(2x)^2 + (3y)^2 = (6sqrt5)^2`

4x² + 9y² = 180     ...(2)

From (1):

x² = 25 − y²

4(25 − y²) + 9y² = 180

100 − 4y² + 9y² = 180

5y² = 80

y² = 16

⇒ y = 4

x² = 25 − 16 = 9

⇒ x = 3

Therefore, the sides of the triangle are:

Smaller side = 3 m

Longer side = 4 m

Hypotenuse = 5 m