Question

solve for x:
61 ft
(5x + 11) ft
11 ft
x =

Explanation:

Step1: Apply the mid - segment theorem of trapezoid

The mid - segment length of a trapezoid is the average of the lengths of the two bases. Let the two bases be \(a = 61\) ft and \(b = 11\) ft, and the mid - segment be \(m=(5x + 11)\) ft. According to the formula \(m=\frac{a + b}{2}\), we have \(5x+11=\frac{61 + 11}{2}\).

Step2: Simplify the right - hand side of the equation

First, calculate \(\frac{61+11}{2}=\frac{72}{2}=36\). So the equation becomes \(5x+11 = 36\).

Step3: Solve for \(x\)

Subtract 11 from both sides of the equation: \(5x=36 - 11\). Then \(5x=25\). Divide both sides by 5: \(x=\frac{25}{5}\).

Answer:

\(x = 5\)