Question

the pair of polygons is similar. find the value of x.
image of two similar rectangles: first rectangle mqrp with length 8x - 1 and width 3x - 1, second rectangle wszv with length 12 and width 4

Explanation:

Step1: Set up proportion for similar rectangles

Since the rectangles are similar, the ratios of corresponding sides are equal. So, $\frac{8x - 1}{12}=\frac{3x - 1}{4}$.

Step2: Cross - multiply

Cross - multiplying gives us $4(8x - 1)=12(3x - 1)$.
Expanding both sides: $32x-4 = 36x-12$.

Step3: Solve for x

Subtract $32x$ from both sides: $- 4=4x - 12$.
Add 12 to both sides: $8 = 4x$.
Divide both sides by 4: $x = 2$.

Answer:

2