Triangle ABC is similar to triangle DEF. Find the measure of side EF. Round your answer to the nearest tenth if necessary. Figures are not drawn to scale.

A 11 C 15 B
E F 40 D

1 answer

First, you need to determine the scale factor between the two triangles. Since they are similar, corresponding sides are proportional.

Let's compare side lengths:
AB to DE, BC to EF, and AC to DF.
Given AB=15 and DE=11, so AB/DE=15/11.
Given BC=40, so EF=40(x).
Given AC=20, so DF=20(x).
Next, you can set up ratios of corresponding sides:
AB/DE=BC/EF=AC/DF.
15/11=40/x=20/x.
Solve for x:
15/11=40/x,
15x = 440,
x = 440/15,
x = 29.3 (rounded to the nearest tenth).
Therefore, the measure of side EF is 29.3 units.