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.
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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!