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? _____

Area Formula Calculation: To find the width of the planter box, we need to use the area formula for a rectangle, which is Area = length × width. We are given the area and the length, so we can solve for the width.Conversion to Improper Fractions: First, let's convert the mixed numbers to improper fractions to make the 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.Setting up Equation: Now, we can set up the equation to solve for the width (w): (31/2) m^2 = (31/4) m × w.Solving for Width: To find w, we divide both sides of the equation by the length (31/4) m: w = (31/2) m^2 ÷ (31/4) m.Dividing Fractions: Dividing the fractions by multiplying by the reciprocal, we get: w = (31/2) m^2 × (4/31) m^(-1).Simplifying Equation: Simplifying the equation, we cancel out the common factor of 31: w = (1/2) m^2 × 4 m^(-1).Final Width Calculation: Multiplying the remaining numbers, we get: w = 2 m. This is the width of the planter box.

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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?
_____

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

\_\_\_\_\_

Area Formula Calculation: To find the width of the planter box, we need to use the area formula for a rectangle, which is $\text{Area} = \text{length} \times \text{width}$ . We are given the area and the length, so we can solve for the width.
Conversion to Improper Fractions: First, let's convert the mixed numbers to improper fractions to make the calculations easier. The area is $15\frac{1}{2}$ m $^2$ , which is $(15\times2 + 1)/2 = \frac{31}{2}$ m $^2$ . The length is $7\frac{3}{4}$ m, which is $(7\times4 + 3)/4 = \frac{31}{4}$ m.
Setting up Equation: Now, we can set up the equation to solve for the width $w$ : $\frac{31}{2} m^2 = \frac{31}{4} m \times w$ .
Solving for Width: To find $w$ , we divide both sides of the equation by the length $(31/4)\,\text{m}$ : $w = (31/2)\,\text{m}^2 \div (31/4)\,\text{m}$ .
Dividing Fractions: Dividing the fractions by multiplying by the reciprocal, we get: $w = \left(\frac{31}{2}\right) m^2 \times \left(\frac{4}{31}\right) m^{-1}$ .
Simplifying Equation: Simplifying the equation, we cancel out the common factor of $31$ : $w = (\frac{1}{2}) m^2 \times 4 m^{-1}$ .
Final Width Calculation: Multiplying the remaining numbers, we get: $w = 2 \, \text{m}$ . This is the width of the planter box.