Question

the following triangles are similar. solve for x
4
6
22.5
x
\frac{x}{4}=\frac{22.5}{6}
\frac{6x}{6}=\frac{90}{6}
x = 15

Explanation:

Step1: Set up proportion

Since the triangles are similar, the ratios of corresponding sides are equal. So, \(\frac{x}{4}=\frac{22.5}{6}\).

Step2: Cross - multiply

Cross - multiplying gives \(6x = 4\times22.5\). Then \(6x=90\).

Step3: Solve for \(x\)

Divide both sides by 6: \(x=\frac{90}{6}\).

Answer:

\(x = 15\)