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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?

1 Answer

May 21, 2016

$Perimeter of △ A B C = 28.8$ $"Perimeter of "triangle ABC = 28.8$

Explanation:

Since $△ A B C$ $triangle ABC$ ~ $△ D E F$ $triangle DEF$

then if $\frac{side of A B C}{corresponding side of D E F} = \frac{3}{5}$ $("side of "ABC)/("corresponding side of "DEF) = 3/5$

$XXX \Rightarrow \frac{perimeter of A B C}{perimeter of D E F} = \frac{3}{5}$ $color(white)("XXX")rArr("perimeter of "ABC)/("perimeter of "DEF) = 3/5$

and since $perimeter of D E F = 48$ $"perimeter of "DEF = 48$

we have
$XXX \frac{perimeter of A B C}{48} = \frac{3}{5}$ $color(white)("XXX")("perimeter of " ABC)/48 =3/5$

$\Rightarrow XXX perimeter of A B C = \frac{3 \times 48}{5} = \frac{144}{5} = 28.8$ $rArrcolor(white)("XXX")"perimeter of "ABC = (3xx48)/5=144/5=28.8$

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