Question

1. triangles abc and def are similar. find x.

Explanation:

Step1: Set up the proportion

Since the triangles are similar, the ratios of corresponding sides are equal. So, \(\frac{11}{7}=\frac{15 + x}{15}\).

Step2: Cross - multiply

Cross - multiplying gives \(11\times15=7\times(15 + x)\).
Which simplifies to \(165 = 105+7x\).

Step3: Solve for \(x\)

Subtract \(105\) from both sides: \(165−105 = 7x\), so \(60 = 7x\).
Then \(x=\frac{60}{7}\approx8.57\).

Answer:

\(8.57\)