Question

The base of an isosceles triangle is 16 cm long. The equal sides are each 22 cm long. Find the height of the triangle.

Answer 1

Given:

The base of an isosceles triangle is 16 cm long.

The equal sides are each 22 cm long.

To find:

The height of the triangle.

Solution:

We know that the altitude of an isosceles triangle divides the base into two equal parts as shown in the below figure.

According to the Pythagoras theorem:

`Hypotenuse^2=Perpendicular^2+Base^2`

Using Pythagoras theorem, we get

`22^2=h^2+8^2`

`484=h^2+64`

`484-64=h^2`

`420=h^2`

Taking square root on both sides, we get

`√(420)=h` (Because side cannot be negative)

`2√(105)=h`

Therefore, the height of the isosceles triangle is
`2√(105)` cm. Approximate height is 20.49 cm.