Find out the answer to "Write and equation then solve for x."

High School
Geometry
High school geometry
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Wierzycaz

Answered question

2021-01-25

Write and equation then solve for x.

Answer & Explanation

Jayden-James Duffy

Skilled2021-01-26Added 91 answers

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

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