Question

Triangle ABC ~ triangle DEF. Use the image to answer the question.

a triangle ABC with side AC labeled 7.93 and a second triangle DEF with side DE labeled 8.8, side FD labeled 6.1 and side EF labeled 6.4

Determine the length of side AB and BC in triangle ABC.

AB = 8.8, BC = 6.4
AB = 7.10, BC = 4.92
AB = 10.56, BC = 7.68
AB = 11.44, BC = 8.32

Answer 1

(d) AB = 11.44, BC = 8.32

Explanation:

You want the measures of sides AB and BC in ∆ABC, which is similar to ∆DEF with DE = 8.8, EF = 6.4, FD = 6.1, when CA = 7.93.

Similar triangles

Corresponding sides are proportional in similar triangles, so we have ...

AB/DE = BC/EF = CA/FD

AB/8.8 = BC/6.4 = 7.93/6.1

Solving for the missing sides gives ...

AB = 8.8(7.93/6.1) = 11.44

BC = 6.4(7.93/6.1) = 8.32

The lengths are AB = 11.44 and BC = 8.32, matching choice D.

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