Solution: Here we shall use the similarity to determine the length of c. In the given figure we know that, FG∥DE (As both the lines are perpendicular to a single line segment GF) Hence, ∠GHD=∼∠GDE Also, ∠G=∼∠G (common angle in both triangles) ∠GFH=∼∠GED (Given) Therefore we can say that △DGE is similar to △HGF Hence, using properties of similarity we can say that, GDGH=DEc 105=8c c=4m Answer: Hence the length of c is 4 m.

Resolved: "Find c. Given:"

High School
Geometry
High school geometry
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Burhan Hopper

Answered question

2021-08-14

Find c.
Given:

Answer & Explanation

Viktor Wiley

Skilled2021-08-15Added 84 answers

Solution:
Here we shall use the similarity to determine the length of c.
In the given figure we know that,
$F G ∥ D E$ (As both the lines are perpendicular to a single line segment GF)
Hence,
$∠ G H D \tilde{=} ∠ G D E$
Also,
$∠ G \tilde{=} ∠ G$ (common angle in both triangles)
$∠ G F H \tilde{=} ∠ G E D$ (Given)
Therefore we can say that $△ D G E$ is similar to $△ H G F$
Hence, using properties of similarity we can say that,
$\frac{G D}{G H} = \frac{D E}{c}$
$\frac{10}{5} = \frac{8}{c}$
c=4m
Answer: Hence the length of c is 4 m.

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