Question

consider two similar triangles, △abc and △def. the three sides lengths, measured in units, of △abc are 13, 15, and 18, and the shortest side length of △def is 15.6 units. what is the perimeter, to the nearest integer unit, of △def?
o 38
o 44
o 55
o 72
o 76

Explanation:

Step1: Find the scale - factor

The shortest side of $\triangle ABC$ is 13 units and the shortest side of $\triangle DEF$ is 15.6 units. The scale - factor $k$ from $\triangle ABC$ to $\triangle DEF$ is $k=\frac{15.6}{13}=1.2$.

Step2: Calculate the perimeter of $\triangle ABC$

The perimeter of $\triangle ABC$, $P_{ABC}=13 + 15+18=46$ units.

Step3: Calculate the perimeter of $\triangle DEF$

Since the ratio of the perimeters of two similar triangles is equal to the scale - factor, the perimeter of $\triangle DEF$, $P_{DEF}=k\times P_{ABC}$. Substituting $k = 1.2$ and $P_{ABC}=46$, we get $P_{DEF}=1.2\times46 = 55.2\approx55$ units.

Answer:

C. 55