Question

i \can\ similarity solve for x. 12 16 x x + 5 a 15 b 18 c 8 d 5 25

Explanation:

Step1: Use the similarity of triangles

Since the two triangles are similar (by AA similarity, as they share an angle and have a right - angle), the ratios of corresponding sides are equal. So, \(\frac{x}{12}=\frac{x + 5}{16}\).

Step2: Cross - multiply

Cross - multiplying gives \(16x=12(x + 5)\).

Step3: Expand the right - side

Expanding \(12(x + 5)\) gives \(16x=12x+60\).

Step4: Solve for \(x\)

Subtract \(12x\) from both sides: \(16x-12x=12x + 60-12x\), so \(4x=60\). Then divide both sides by \(4\): \(x = 15\).

Answer:

A. 15