# The perimeter of an isosceles triangle is 29 feet. If the base measures 15 feet what is the measure of the other two sides?

Mar 25, 2018

They each equal $7$ feet.

#### Explanation:

The equation for the perimeter of a triangle is $P = {S}_{1} + {S}_{2} + {S}_{3}$,
which for an isosceles triangle could be written as: $P = {S}_{1} + 2 \left({S}_{2}\right)$
We know the perimeter is $29$ feet, and the base is $15$ feet. So we can substitute in those values to get:

$\implies$$29 = 15 + 2 \left({S}_{2}\right)$

Subtract $15$ from both sides, and get:

$\implies$$14 = 2 \left({S}_{2}\right)$

Divide by $2$, and get:

$\implies$$7 = {S}_{2}$

Since ${S}_{2} = {S}_{3}$, we know that both sides equal $7$ feet, which makes since, as it is an isosceles triangle and $7 + 7 + 15 = 29$.