Question

The altitude to the hypotenuse of a right triangle divides the hypotenuse into two segments measuring 11 cm and 5 cm. To the nearest tenth, what is the length of the shorter leg of the triangle?

Answer 1

8.4 cm

Explanation:

Given that:

A right angled triangle, let
`\triangle ABD`. Right angled at
`\angle A`.

Altitude AC to the hypotenuse BD.

Length of side BC = 5 cm

Length of side CD = 11 cm

We have to find the value of shorter leg of triangle. i.e. side AB = ?

Using the concept of similarity, we can say the following:

`(AB)/(BC) = (BD)/(AB)\\\Rightarrow AB^2=BC.BD\\\Rightarrow AB^2=5* (5+11)\\\Rightarrow AB^2=5* 16\\\Rightarrow AB^2=80\\\Rightarrow AB=√(80)\\\Rightarrow \bold{AB\approx 8.4\ cm}`

The length of shorter leg of the triangle = 8.4 cm