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The, area of the rectangle below is
8(1)/(4) square inches. Find the perimeter. Show your work.

Width is 4(1)/(2)in.

$7$ $-20$ . The, area of the rectangle below is $8 \frac{1}{4}$ square inches. Find the perimeter. Show your work. $\newline$ Width is $4 \frac{1}{2} \mathrm{in}$ .

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Find the roots of factored polynomials

Full solution

Q.

7

-20

. The, area of the rectangle below is

8 \frac{1}{4}

square inches. Find the perimeter. Show your work.

\newline

Width is

4 \frac{1}{2} \mathrm{in}

.

Find Perimeter: To find the perimeter of a rectangle, we need to know both the length and the width. We already have the length, which is $4\frac{1}{2}$ inches. We can find the width by dividing the area by the length.
Convert to Fractions: First, let's convert the mixed numbers to improper fractions to make the calculations easier. The area is $8 \frac{1}{4}$ square inches, which is $(8\times 4 + 1)/4 = \frac{33}{4}$ square inches. The length is $4 \frac{1}{2}$ inches, which is $(4\times 2 + 1)/2 = \frac{9}{2}$ inches.
Calculate Width: Now, we divide the area by the length to find the width: $(33/4) / (9/2) = (33/4) \times (2/9) = 33/18 = 11/6$ inches. This is the width of the rectangle.
Perimeter Formula: The perimeter of a rectangle is given by the formula $P = 2(l + w)$ , where $l$ is the length and $w$ is the width. We have $l = \frac{9}{2}$ inches and $w = \frac{11}{6}$ inches.
Add Fractions: Let's calculate the perimeter: $P = 2\left[\left(\frac{9}{2}\right) + \left(\frac{11}{6}\right)\right]$ . First, we need a common denominator to add the fractions. The common denominator for $2$ and $6$ is $6$ .
Find Common Denominator: Convert the length to a fraction with a denominator of $6$ : $(\frac{9}{2}) \times (\frac{3}{3}) = \frac{27}{6}$ inches. $\newline$ Now we can add the length and width: $(\frac{27}{6}) + (\frac{11}{6}) = \frac{38}{6}$ inches.
Multiply by $2$ : Multiply the sum by $2$ to find the perimeter: $P = 2 \times \left(\frac{38}{6}\right) = \frac{76}{6}$ inches.
Simplify Fraction: Simplify the fraction: $\frac{76}{6} = 12 \frac{4}{6}$ inches, and $\frac{4}{6}$ can be simplified to $\frac{2}{3}$ , so the perimeter is $12 \frac{2}{3}$ inches.

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