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Use the formula \( P=2 w+2 l \) to find \( P \). \( I=\frac{5}{8} \) foot and \( w=\frac{1}{4} \) foot The perimeter is \( \square \) feet.

Ask by May Weston. in the United States
Feb 27,2025

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Tutor-Verified Answer

Answer

The perimeter \( P \) is \( 1\frac{3}{4} \) feet or 1.75 feet.

Solution

Given: - \( I = \frac{5}{8} \) foot - \( w = \frac{1}{4} \) foot The formula for the perimeter \( P \) is given by: \[ P = 2w + 2l \] Substitute the given values into the formula: \[ P = 2\left(\frac{1}{4}\right) + 2\left(\frac{5}{8}\right) \] Now, we can calculate the perimeter \( P \) by simplifying the expression. Calculate the value by following steps: - step0: Calculate: \(2\times \frac{1}{4}+2\times \frac{5}{8}\) - step1: Multiply the numbers: \(\frac{1}{2}+2\times \frac{5}{8}\) - step2: Multiply the numbers: \(\frac{1}{2}+\frac{5}{4}\) - step3: Reduce fractions to a common denominator: \(\frac{2}{2\times 2}+\frac{5}{4}\) - step4: Multiply the numbers: \(\frac{2}{4}+\frac{5}{4}\) - step5: Transform the expression: \(\frac{2+5}{4}\) - step6: Add the numbers: \(\frac{7}{4}\) The perimeter \( P \) is \( 1\frac{3}{4} \) feet or 1.75 feet.

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The Deep Dive

To find the perimeter \( P \) using the formula \( P = 2w + 2l \), we first need to determine the value of \( l \). Given that \( I = \frac{5}{8} \) foot represents the total length of both length sides, so we know that \( l = I - w \). Substituting \( w = \frac{1}{4} \) foot into \( l \): \[ l = \frac{5}{8} - \frac{1}{4} = \frac{5}{8} - \frac{2}{8} = \frac{3}{8} \text{ feet}. \] Now plug \( w \) and \( l \) into the perimeter formula: \[ P = 2(\frac{1}{4}) + 2(\frac{3}{8}) = \frac{2}{4} + \frac{6}{8} = \frac{1}{2} + \frac{3}{4} = \frac{2}{4} + \frac{3}{4} = \frac{5}{4} \text{ feet}. \] The perimeter is \( \frac{5}{4} \) feet or \( 1.25 \) feet. Wouldn't it be fun to visualize this? Imagine drawing a rectangle based on these dimensions: a width of \( \frac{1}{4} \) foot and a length of \( \frac{3}{8} \) foot! That's around the size of a classic postcard! And speaking of perimeters, calculating them is crucial in everyday life, like when you're framing a new garden or deciding how much fencing you need. It’s as easy as pie, you just have to remember to double your widths and lengths! Keeping track of units is super important though; keep those fractions tidy!

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