Question

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

Explanation:

Step1: Use the property of similar triangles

For similar triangles \(ABC\) and \(DEF\), the ratios of corresponding sides are equal. So, \(\frac{AB}{DE}=\frac{AC}{DF}\).

Step2: Substitute the given values

Given \(AB = 11\), \(DE=7\), \(AC=15 + x\), and \(DF = 15\). Then \(\frac{11}{7}=\frac{15 + x}{15}\).

Step3: Cross - multiply

Cross - multiplying gives \(11\times15=7\times(15 + x)\).

Step4: Expand and simplify

\(165 = 105+7x\). Subtract \(105\) from both sides: \(165−105 = 7x\), so \(60 = 7x\).

Step5: Solve for \(x\)

Divide both sides by \(7\): \(x=\frac{60}{7}\approx8.57\).

Answer:

\(8.57\)