Question

If the scale factor for two similar triangles is 4:3, and the perimeter of the smaller triangle is 36 inches, what is the perimeter of the larger triangle?

Answer 1

To find the perimeter of the larger triangle, we can use the properties of similar triangles. The scale factor between the two triangles is given as 4:3, meaning that the ratio of corresponding sides (and also the perimeter, since all sides are proportional) is 4 to 3.

Let \( P_s \) be the perimeter of the smaller triangle and \( P_l \) be the perimeter of the larger triangle. Given that \( P_s = 36 \) inches, we can set up the proportion based on the scale factor:

\[
\frac{P_l}{P_s} = \frac{4}{3}
\]

Substituting the value of \( P_s \):

\[
\frac{P_l}{36} = \frac{4}{3}
\]

To solve for \( P_l \), we can cross-multiply:

\[
3P_l = 4 \times 36
\]

Calculating \( 4 \times 36 \):

\[
4 \times 36 = 144
\]

So we have:

\[
3P_l = 144
\]

Now, divide both sides by 3:

\[
P_l = \frac{144}{3} = 48
\]

Thus, the perimeter of the larger triangle is

\[
\boxed{48} \text{ inches}.
\]