Question

find the value of x .
f 8 in. e
a
x in. 12 in.
d
b 6 in. c
x = \square

Explanation:

Step1: Identify similar triangles

Triangles \(ABC\) and \(DEF\) are similar (by AA similarity, as both have a right - angle and one equal non - right angle).

Step2: Set up proportion

For similar triangles, the ratios of corresponding sides are equal. So, \(\frac{BC}{EF}=\frac{AC}{DF}\). Substituting the values: \(\frac{6}{8}=\frac{x}{12}\).

Step3: Solve for \(x\)

Cross - multiply: \(8x = 6\times12\). Then \(8x=72\). Divide both sides by \(8\): \(x=\frac{72}{8}=9\).

Answer:

\(9\)