Question

1. members of a landscaping company built a retaining wall. they used brick to make the top \\(\frac{2}{3}\\) of the wall. \\(2\frac{3}{4}\\) feet \\(8\frac{1}{2}\\) feet a. what is the height of the brick portion of the wall? write an equation to model your work. b. estimate the area of the whole retaining wall. c. what is the area of the whole retaining wall? write an equation to show your work. compare your answer to your estimate to see if your answer is reasonable.

Explanation:

Step1: Convert mixed numbers to fractions

Whole wall height: $2\frac{3}{4} = \frac{11}{4}$ ft; Wall width: $8\frac{1}{2} = \frac{17}{2}$ ft

Step2: Solve for brick height (Part A)

Multiply total height by $\frac{2}{3}$
$\text{Brick height} = \frac{2}{3} \times \frac{11}{4} = \frac{22}{12} = \frac{11}{6} = 1\frac{5}{6}$ ft

Step3: Estimate wall area (Part B)

Round dimensions: $2\frac{3}{4} \approx 3$ ft, $8\frac{1}{2} \approx 9$ ft
$\text{Estimated Area} = 3 \times 9 = 27$ sq ft

Step4: Calculate exact wall area (Part C)

Multiply width by total height
$\text{Exact Area} = \frac{17}{2} \times \frac{11}{4} = \frac{187}{8} = 23\frac{3}{8}$ sq ft
Compare to estimate: $23\frac{3}{8}$ is close to 27, so reasonable.

Answer:

A. Equation: $\text{Brick Height} = \frac{2}{3} \times 2\frac{3}{4}$; Height = $1\frac{5}{6}$ feet
B. Estimated Area = 27 square feet
C. Equation: $\text{Total Area} = 8\frac{1}{2} \times 2\frac{3}{4}$; Exact Area = $23\frac{3}{8}$ square feet. This is close to the 27 sq ft estimate, so the answer is reasonable.