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romanna [79]
2 years ago
7

In the diagram below, GH is parallel to DE . If GH is 3 more than EH FH=10, and DE=12 find the length of EH. Figures are not nec

essarily drawn to scale. State your answer in simplest radical form, if necessary.

Mathematics
1 answer:
steposvetlana [31]2 years ago
6 0

Answer: 5

Step-by-step explanation:

Since \overline{GH} \parallel \overline{DE}, by the corresponding angles theorem, \angle FGH \cong \angle FDE, \angle FHG \cong \angle FED. This means \triangle FGH \sim \triangle FDE by AA.

As corresponding sides of similar triangles are proportional,

\frac{10}{x+3}=\frac{10+x}{12}\\(10)(12)=(10+x)(x+3)\\120=x^{2}+13x+30\\x^{2}+13x-90=0\\(x+18)(x-5)=0\\x=-18, 5
However, as distance must be positive, we consider the positive solution, x=5.

Therefore, the answer is <u>5</u>

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