Question

In the diagram below, start overline, D, E, end overline
DE
is parallel to start overline, A, B, end overline
AB
. Solve for xx. Round your answer to the nearest tenth if necessary. CD is 22.2, CE is 17.8, DA is 17.8, and EB is x.

Answer 1

Because DE || AB, triangles CDE and CAB are similar. So corresponding side ratios are equal:

CD/CA = CE/CB.

CA = CD + DA = 22.2 + 17.8 = 40.0, and CB = CE + EB = 17.8 + x. Thus

22.2/40 = 17.8/(17.8 + x).

Solve:
0.555 = 17.8/(17.8 + x)
0.555(17.8 + x) = 17.8
9.879 + 0.555x = 17.8
0.555x = 7.921
x = 7.921/0.555 ≈ 14.3.

So x ≈ 14.3.