# Perimeter of an isosceles triangle is 71 centimeters. The measure of one of the sides is 22 centimeters. What are all the possible measure of the other two side?

Nov 3, 2016

Possible measures of the other two sides are either, $22 c m$ and $27 c m ,$ or , $22 c m$ and $24.5 c m$ respectively.

#### Explanation:

An isosceles triangle have two sides of equal length, and another side of another length.

$\therefore$ There are two measures possible for the other two sides.

• Possibility 1.
$22 c m$ is the measure of two equal sides.
$\therefore$Let, $x$ be the measure of the other side.
$\therefore$ Perimeter $= \left(22 + 22 + x\right) c m = \left(44 + x\right) c m = 71 c m .$
$\therefore x = 27 c m .$

• Possibility 2.
$22 c m$ is the measure of one unequal side.
$\therefore$ Let, $x$ be the measure of two equal sides each.
$\therefore$ Perimeter $=$ $\left(22 + x + x\right) c m = \left(22 + 2 x\right) c m = 71 c m .$
$\therefore 2 x = 49 c m .$
$\therefore x = 24.5 c m .$

Therefore, possible measures of the other two sides are either, $22 c m$ and $27 c m ,$ or , $22 c m$ and $24.5 c m$ respectively. (answer)

Note : To know more about isosceles triangle, please check into :
https://en.wikipedia.org/wiki/Isosceles_triangle.