Question

you estimate that the length of the garden is 13 feet and the width is 7 feet, but you decide to measure the exact dimensions instead so that you can purchase the right amount of materials. with a tape measure, you determine that the length is 12 feet and the width is 6 feet. how does the actual perimeter of the garden compare with your estimate? the actual perimeter is 10 feet longer than your estimate. the actual perimeter is 4 feet longer than your estimate. the actual perimeter is 10 feet shorter than your estimate. the actual perimeter is 4 feet shorter than your estimate.

Explanation:

Step1: Calculate the estimated perimeter

The formula for the perimeter of a rectangle is \(P = 2(l + w)\). For the estimated values \(l = 13\) feet and \(w = 7\) feet, we have \(P_{estimated}=2(13 + 7)=2\times20 = 40\) feet.

Step2: Calculate the actual perimeter

For the actual values \(l = 12\) feet and \(w = 6\) feet, using the same formula \(P = 2(l + w)\), we get \(P_{actual}=2(12 + 6)=2\times18 = 36\) feet.

Step3: Find the difference between the perimeters

Subtract the actual perimeter from the estimated perimeter: \(P_{estimated}-P_{actual}=40 - 36=4\) feet.

Answer:

The actual perimeter is 4 feet shorter than your estimate.