Question

the pair of polygons is similar. find the value of x.
x + 1
3x + 1
8
20
x =

Explanation:

Step1: Set up proportion

Since the polygons are similar, the ratios of corresponding sides are equal. Let's assume the corresponding - side ratio gives us the equation $\frac{x + 1}{8}=\frac{3x + 1}{20}$.

Step2: Cross - multiply

Cross - multiplying the proportion $ \frac{x + 1}{8}=\frac{3x + 1}{20}$ gives us $20(x + 1)=8(3x + 1)$.

Step3: Expand both sides

Expand the left - hand side: $20x+20$, and the right - hand side: $24x + 8$. So, $20x+20 = 24x+8$.

Step4: Isolate the variable terms

Subtract $20x$ from both sides: $20=24x - 20x+8$, which simplifies to $20 = 4x+8$.

Step5: Solve for x

Subtract 8 from both sides: $4x=20 - 8$, so $4x = 12$. Then divide both sides by 4: $x=\frac{12}{4}=3$.

Answer:

$3$