Question

The scale factor for two similar triangles is 2:3. The perimeter of the smaller triangle is 56 cm. What is the perimeter of the larger triangle in centimeters?

Short answer

The perimeter of larger triangle is $84\mathrm{cm}$.

Step-by-step solution

Step 1. Perimeter of a triangle.

The basic formula to calculate the perimeter of a triangle with sides 'a', 'b', and 'c' is:$a+b+c$

Step 2. Use given information and determine the equation.

Let the perimeter of larger triangle be x.

Scale factor of two triangles is $2:3.$

Perimeter of smaller triangle$56\mathrm{cm}$

$\frac{2}{3}=\frac{56}{x}$

Step 3. Solve for x.

The equation can be written as:

$\begin{array}{l}\frac{2}{3}=\frac{56}{x}\\ 2x=56\times 3\\ 2x=168\\ x=84\mathrm{cm}.\end{array}$.

Hence, the perimeter of larger triangle is$84\mathrm{cm}.$