Question

one leg of a right triangle is twice as long as the other leg, If the hypotenuse side is 5cm long then what is the measure of the shorter leg (you can leave your answer as a decimal or in radical form)

Answer 1

The shorter leg is
`√(5) \ cm`

Explanation:

Let the base be x and the perpendicular be y.

It is given that, one leg of a right triangle is twice as long as the other leg,

y = 2x ...(1)

Hypotenuse, H = 5 cm

We can use Pythagoras theorem as follows :

`H^2=B^2+P^2`

Putting all the values,

`5^2=x^2+(2x)^2\\\\25=x^2+4x^2\\\\25=5x^2\\\\x^2=5\\\\x=√(5)\ cm`

So, the base is
`\sqrt5\ cm`. No, to find the value of y put x in equation (1). So,

`y=2x\\\\=2√(5) \ cm`

Hence, the measure of the shorter leg is
`√(5) \ cm`