Question

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

Explanation:

Step1: Identify corresponding sides

Since the polygons are similar, corresponding sides are proportional. The sides \(JW = x + 1\) and \(SR = 8\), \(JC = 3x + 1\) and \(RP = 20\) are corresponding. So we set up the proportion \(\frac{x + 1}{8}=\frac{3x + 1}{20}\).

Step2: Cross - multiply

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

Step3: Expand both sides

Expanding, we get \(20x+20 = 24x + 8\).

Step4: Solve for x

Subtract \(20x\) from both sides: \(20=4x + 8\). Then subtract 8 from both sides: \(12 = 4x\). Divide both sides by 4: \(x = 3\).

Answer:

\(x = 3\)