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Gabriel is designing a rectangular planter box for their garden. It needs to cover an area of $15\frac{1}{5}\,\text{m}^2$ . Gabriel wants it to be $7\frac{3}{4}$ long. How wide does the planter box need to be?

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Area and perimeter: word problems

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Q. Gabriel is designing a rectangular planter box for their garden. It needs to cover an area of

15\frac{1}{5}\,\text{m}^2

. Gabriel wants it to be

7\frac{3}{4}

long. How wide does the planter box need to be?

Convert to Improper Fractions: Convert the mixed numbers to improper fractions for easier calculation. $\newline$ Area of the planter box: $15 \frac{1}{5} \text{ m}^2 = \left(15 \times 5 + 1\right)/5 = \frac{76}{5} \text{ m}^2$ $\newline$ Length of the planter box: $7 \frac{3}{4} \text{ m} = \left(7 \times 4 + 3\right)/4 = \frac{31}{4} \text{ m}$
Calculate Width: Use the formula for the area of a rectangle $\text{Area} = \text{Length} \times \text{Width}$ to find the width. $\newline$ Let $w$ be the width of the planter box. $\newline$ $\text{Area} = \text{Length} \times \text{Width}$ $\newline$ $\frac{76}{5} = \frac{31}{4} \times w$
Solve for Width: Solve for $w$ by dividing both sides of the equation by the length. $w = \frac{76}{5} / \frac{31}{4}$ $w = \frac{76}{5} \times \frac{4}{31}$ $w = \frac{304}{155}$
Find Width in Meters: Simplify the fraction to find the width in meters. $\newline$ $w = \frac{304}{155}$ $\newline$ $w = 1 \frac{149}{155} \, \text{m}$

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