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

Explanation:

Let x be the other leg or the base and the first leg is y or the perpendicular. ATQ,

One leg of a right triangle is twice as long as the other leg,

y = 2x

Hypotenuse, H = 5 cm

For a right angled triangle, using Pythagoras theorem,

`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`

Other leg,

`y=2x\\\\=2√(5) \ cm`

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