Question

the two trapezoids are similar. create and solve a proportion to find the value of x. x = 40 35 45 35 16 2x + 4

Explanation:

Step1: Set up the proportion

Since the two trapezoids are similar, the ratios of their corresponding sides are equal. So, we have the proportion \(\frac{40}{16}=\frac{45}{2x + 4}\).

Step2: Cross - multiply

Cross - multiplying gives us \(40\times(2x + 4)=16\times45\).
Expanding the left - hand side: \(80x+160 = 720\).

Step3: Solve for \(x\)

Subtract \(160\) from both sides: \(80x=720 - 160\), so \(80x = 560\).
Divide both sides by \(80\): \(x=\frac{560}{80}\).

Answer:

\(x = 7\)