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

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06-06-2022
Mathematics

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

Sagot :

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Medunno13 Medunno13 · Answer 1 · 2022-06-06T21:06:12-04:00

Answer: 5

Step-by-step explanation:

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

As corresponding sides of similar triangles are proportional,

[tex]\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[/tex]
However, as distance must be positive, we consider the positive solution, x=5.

Therefore, the answer is 5

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

Sagot :

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