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Write and equation then solve for x.12210107101.jpg

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asked 2021-01-25

Write and equation then solve for x.
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Answers (1)

2021-01-26

Step 1
We will use similarity of the given two triangles to find the value of x.
Step 2
\(\displaystyle\angle{B}{A}{E}\stackrel{\sim}{=}\angle{C}{A}{D}\) (same angle)
\(\displaystyle\angle{B}{E}{A}\stackrel{\sim}{=}\angle{C}{D}{A}\) (\(\displaystyle{90}^{\circ}\) both)
Hence \(\displaystyle\triangle{A}{E}{B}\sim\triangle{A}{D}{C}\)
Hence \(\displaystyle\frac{{{B}{E}}}{{{C}{D}}}=\frac{{{A}{B}}}{{{A}{C}}}\)
\(\displaystyle\Rightarrow\frac{{x}}{{15}}=\frac{{12}}{{{12}+{6}}}\)
\(\displaystyle\Rightarrow\frac{{x}}{{15}}=\frac{{12}}{{18}}\)
\(\displaystyle\Rightarrow{x}=\frac{{{12}\times{15}}}{{18}}\)
\(=10\)
Hence \(x = 10 cm\)

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