Question

the pair of polygons is similar. find the value of x. x =

Explanation:

Step1: Set up proportion

Since the polygons are similar, the ratios of corresponding sides are equal. So, \(\frac{3x + 1}{20}=\frac{x + 1}{8}\).

Step2: Cross - multiply

Cross - multiplying gives \(8(3x + 1)=20(x + 1)\).

Step3: Expand

Expand both sides: \(24x+8 = 20x + 20\).

Step4: Solve for \(x\)

Subtract \(20x\) from both sides: \(24x-20x+8=20x-20x + 20\), which simplifies to \(4x+8 = 20\). Then subtract \(8\) from both sides: \(4x+8 - 8=20 - 8\), so \(4x=12\). Divide both sides by \(4\): \(x=\frac{12}{4}=3\).

Answer:

\(3\)