Given:DE = 5, AC = 28, EC = BC Find:BC (Enter your answers as a comma-separated list.)

Question

△ADE ~ △ABC.

Given:DE = 5, AC = 28, EC = BC

Find:BC

(Enter your answers as a comma-separated list.)

Answer 1

DE=5

AC=28

EC=BC

EA+EC=28

Let EC=BC=x

Then, EA = 28-x

From similar triangles, EA/DE = AC/BC

Substituting, 28-x/5 = 28/x

Cross-multiplying, 28x-x^2 = 140

x^2 - 28x + 140 = 0

x = 14 ± 2√14

14-2√14, 14+2√14