Question

Write and equation then solve for x.12210107101.jpg

Similarity

Write and equation then solve for x.

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 $$x = 10 cm$$