Question

The ratio of the sides of two triangles is 6:7. If the perimeter of the smaller triangle is 72 feet, find the perimeter of the larger triangle.

Answer 1

The perimeter is the sum of all sides, therefore:

Let:

P1 = Perimeter of the smaller triangle

P2 = Perimeter of the larger triangle

so:

$\begin{gathered} P1=a+b+c \\ P2=A+B+C \\ a\colon A=b\colon B=c\colon C=\frac{a}{A}=\frac{b}{B}=\frac{c}{C}=\frac{6}{7} \\ so\colon \\ P2=\frac{6}{7}a+\frac{6}{7}b+\frac{6}{7}c=72 \\ so\colon \\ P2=72\cdot\frac{7}{6} \\ P2=84ft \end{gathered}$