Question

an isosceles trapezoid has a perimeter of 38 miles. its shorter base measures 4 miles and its longer base measures 6 miles. the two remaining sides have the same length; what is that length?
□ miles
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Explanation:

Step1: Recall the perimeter formula for a trapezoid

The perimeter \( P \) of a trapezoid is the sum of all its sides. For an isosceles trapezoid, the formula is \( P = a + b + 2c \), where \( a \) and \( b \) are the lengths of the two bases, and \( c \) is the length of each of the two equal non - parallel sides.

Step2: Substitute the known values into the formula

We know that \( P = 38 \) miles, \( a = 4 \) miles (shorter base), and \( b = 6 \) miles (longer base). Substituting these values into the formula \( 38=4 + 6+2c \).

Step3: Simplify the equation

First, simplify the right - hand side of the equation: \( 4 + 6=10 \), so the equation becomes \( 38 = 10+2c \).

Step4: Solve for \( c \)

Subtract 10 from both sides of the equation: \( 38-10=2c \), which gives \( 28 = 2c \). Then divide both sides by 2: \( c=\frac{28}{2}=14 \) miles.

Answer:

14