Question

In the diagram below, angle, F, E, D, \cong, angle, F, H, G∠FED≅∠FHG. G, D, equals, 11, point, 7GD=11.7, H, E, equals, 6, point, 7HE=6.7, and F, G, equals, 23, point, 3FG=23.3. Find the length of start overline, F, H, end overline
FH
. Round your answer to the nearest tenth if necessary.

Answer 1

Triangles FED and FHG are similar (∠F is common and ∠FED ≅ ∠FHG), so corresponding sides are in proportion:
FE/FH = FD/FG.

From the diagram F–G–D are collinear with GD = 11.7 and FG = 23.3, so FD = FG + GD = 23.3 + 11.7 = 35.0.
Also F–H–E are collinear with HE = 6.7, so FE = FH + 6.7.

Substitute into the proportion:
(FH + 6.7)/FH = 35.0/23.3.

Solve for FH:
1 + 6.7/FH = 35.0/23.3
6.7/FH = 35.0/23.3 − 1 = 11.7/23.3
FH = 6.7 / (11.7/23.3) = 6.7 * 23.3 / 11.7 ≈ 13.3.

So FH ≈ 13.3 (to the nearest tenth).