Question

a rectangle has a perimeter of 38 feet and a base of 13 feet. what is the height?
feet
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Explanation:

Step1: Recall perimeter formula for rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{base} + \text{height}) \), or \( P = 2b + 2h \), where \( b \) is the base and \( h \) is the height.

Step2: Substitute known values into formula

We know \( P = 38 \) feet and \( b = 13 \) feet. Substitute these into the formula: \( 38 = 2\times13 + 2h \).

Step3: Simplify and solve for \( h \)

First, calculate \( 2\times13 = 26 \). So the equation becomes \( 38 = 26 + 2h \). Subtract 26 from both sides: \( 38 - 26 = 2h \), which simplifies to \( 12 = 2h \). Then divide both sides by 2: \( h = \frac{12}{2} = 6 \).

Answer:

6