# The ratio of the side lengths of an isosceles triangle is 4:4:7, and its perimeter is 52.5cm. What is the length of the base of the triangle?

Aug 2, 2016

$24 \frac{1}{2} \to 24.5$

#### Explanation:

The given values of $4 : 4 : 7$ are a ratio consisting of a total count of
$4 + 4 + 7 = 15$ parts

As this is an Isosceles triangle the base is 7. However the 7 parts is out of 15 parts. So as a fraction of the whole perimeter it is $\frac{7}{15}$

Thus the length of the base of the triangle is:

$\frac{7}{15} \times 52 \frac{1}{2}$

$\frac{7}{{\cancel{15}}^{1}} \times \frac{{\cancel{105}}^{7}}{2} \text{ "=" "49/2" "=" } 24 \frac{1}{2}$