Question

The hypotenuse of a right triangle is 15cm long. One of the triangle’s legs is two times the length of the other leg. Find the lengths of the three sides of the triangle

Answer 1

15, 3
`√(5)` and 6
`√(5)`

Explanation:

Since the triangle is right use Pythagoras' identity to solve.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let one leg be x then the other leg is 2x, then

x² + (2x)² = 15², that is

x² + 4x² = 225

5x² = 225 ( divide both sides by 5 )

x² = 45 ( take the square root of both sides )

x =
`√(45)` =
`√(9(5))` = 3
`√(5)`

The other leg is 2 × 3
`√(5)` = 6
`√(5)`

Answer 2

6.7cm, 13.4cm, 15cm.

Explanation:

Let x be one side of the triangle. The question tells us the other side is 2x.

We can relate all 3 sides using the Pythagorean Theorem:

`15^2=x^2+(2x)^2\\225=x^2+4x^2\\225=5x^2\\x^2=45\\x=6.7`

That means the side lengths are 6.7cm and 2 x 6.7 cm = 13.4cm.