Gabriel is designing a rectangular planter box for their garden. It needs to cover an area of 15 1/5m2 . Gabriel wants it to be 7 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. Area of the planter box: 15 1/5 m² = (15 * 5 + 1)/5 = 76/5 m² Length of the planter box: 7 3/4 m = (7 * 4 + 3)/4 = 31/4 mCalculate Width: Use the formula for the area of a rectangle (Area = Length * Width) to find the width. Let w be the width of the planter box. Area = Length * Width 76/5 = (31/4) * wSolve for Width: Solve for w by dividing both sides of the equation by the length. w = (76/5) / (31/4) w = (76/5) * (4/31) w = 304/155Find Width in Meters: Simplify the fraction to find the width in meters. w = 304/155 w = 1 149/155 m

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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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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. $\newline$ $w = \frac{304}{155}$ $\newline$ $w = 1 \frac{149}{155} \, \text{m}$