Question

find the value of n.
top base: 3.8 in
two equal sides: n
bottom base: 11.4 in
perimeter = 29.1 inches
n = inches

Explanation:

Step1: Recall the perimeter formula for a trapezoid

The perimeter \( P \) of a trapezoid is the sum of all its sides. For this trapezoid, the sides are \( 3.8 \) miles, \( 11.4 \) miles, and two sides of length \( n \). So the formula is \( P = 3.8 + 11.4 + n + n \).

Step2: Substitute the given perimeter

We know the perimeter \( P = 29.4 \) miles. Substituting into the formula: \( 29.4 = 3.8 + 11.4 + 2n \).

Step3: Simplify the right - hand side

First, calculate \( 3.8+11.4 = 15.2 \). So the equation becomes \( 29.4=15.2 + 2n \).

Step4: Solve for \( n \)

Subtract \( 15.2 \) from both sides: \( 29.4 - 15.2=2n \). \( 14.2 = 2n \). Then divide both sides by \( 2 \): \( n=\frac{14.2}{2}=7.1 \).

Answer:

\( 7.1 \)