Gabriel is designing a rectangular planter box for their garden. It needs to cover an area of 15(1)/(2)m^(2). Gabriel wants it to be 7(3)/(4)m long. How wide does the planter box need to be? m

Understand Relationship and Area Calculation: Understand the relationship between the length, width, and area of a rectangle. The area of a rectangle is calculated by multiplying its length by its width. Area = Length × Width We are given the area and the length, so we can solve for the width.Convert Mixed Numbers to Improper Fractions: Convert the mixed numbers to improper fractions to make calculations easier. The area is 15(1)/(2) m^2, which is (15*2 + 1)/2 = 31/2 m^2. The length is 7(3)/(4) m, which is (7*4 + 3)/4 = 31/4 m.Use Area Formula to Solve: Use the area formula to solve for the width. Let W be the width of the planter box. Area = Length × Width 31/2 m^2 = (31/4 m) × WDivide Equation to Find Width: Divide both sides of the equation by the length to solve for the width. W = (31/2 m^2) / (31/4 m)Perform Division by Reciprocal: Perform the division by multiplying by the reciprocal of the length. W = (31/2 m^2) × (4/31 m)Simplify Expression: Simplify the expression by canceling out common factors. The 31 in the numerator and denominator cancels out, as does one m from m^2 and m, leaving us with: W = (1/2) × 4Calculate Final Width: Calculate the width. W = 2 m

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Gabriel is designing a rectangular planter box for their garden. It needs to cover an area of
15(1)/(2)m^(2). Gabriel wants it to be
7(3)/(4)m long.
How wide does the planter box need to be?
m

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

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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}{2} \mathrm{~m}^{2}

. Gabriel wants it to be

7 \frac{3}{4} \mathrm{~m}

long.

\newline

How wide does the planter box need to be?

\newline

Understand Relationship and Area Calculation: Understand the relationship between the length, width, and area of a rectangle. $\newline$ The area of a rectangle is calculated by multiplying its length by its width. $\newline$ Area $= Length \times Width$ $\newline$ We are given the area and the length, so we can solve for the width.
Convert Mixed Numbers to Improper Fractions: Convert the mixed numbers to improper fractions to make calculations easier. $\newline$ The area is $15\frac{1}{2} \text{ m}^2$ , which is $(15\times 2 + 1)/2 = \frac{31}{2} \text{ m}^2$ . $\newline$ The length is $7\frac{3}{4} \text{ m}$ , which is $(7\times 4 + 3)/4 = \frac{31}{4} \text{ m}.$
Use Area Formula to Solve: Use the area formula to solve for the width. $\newline$ Let $W$ be the width of the planter box. $\newline$ Area $= \text{Length} \times \text{Width}$ $\newline$ $\frac{31}{2} \, \text{m}^2 = \left(\frac{31}{4} \, \text{m}\right) \times W$
Divide Equation to Find Width: Divide both sides of the equation by the length to solve for the width. $W = \frac{\frac{31}{2} m^2}{\frac{31}{4} m}$
Perform Division by Reciprocal: Perform the division by multiplying by the reciprocal of the length. $\newline$ $W = \left(\frac{31}{2} m^2\right) \times \left(\frac{4}{31} m\right)$
Simplify Expression: Simplify the expression by canceling out common factors. $\newline$ The $31$ in the numerator and denominator cancels out, as does one $m$ from $m^2$ and $m$ , leaving us with: $\newline$ $W = (\frac{1}{2}) \times 4$
Calculate Final Width: Calculate the width. $W = 2\,\text{m}$