# The ratio of one side of Triangle ABC to the corresponding side of similar Triangle DEF is 3:5. If the perimeter of Triangle DEF is 48 inches, what is the perimeter of Triangle ABC?

May 21, 2016

$\text{Perimeter of } \triangle A B C = 28.8$

#### Explanation:

Since $\triangle A B C$ ~ $\triangle D E F$

then if $\left(\text{side of "ABC)/("corresponding side of } D E F\right) = \frac{3}{5}$

$\textcolor{w h i t e}{\text{XXX")rArr("perimeter of "ABC)/("perimeter of } D E F} = \frac{3}{5}$

and since $\text{perimeter of } D E F = 48$

we have
$\frac{\textcolor{w h i t e}{\text{XXX")("perimeter of } A B C}}{48} = \frac{3}{5}$

rArrcolor(white)("XXX")"perimeter of "ABC = (3xx48)/5=144/5=28.8