Question

1. members of a company built a retaining wall. they used brick to make the top $\frac{2}{3}$ of the wall.$2\frac{3}{4}$ feet$8\frac{1}{2}$ feeta. 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: $2\frac{3}{4} = \frac{11}{4}$ feet; Width: $8\frac{1}{2} = \frac{17}{2}$ feet

Step2: Calculate brick portion height (Part A)

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

Step3: Estimate wall area (Part B)

Round values: $2\frac{3}{4} \approx 3$, $8\frac{1}{2} \approx 9$
$\text{Estimated Area} = 3 \times 9 = 27$ square feet

Step4: Calculate exact wall area (Part C)

Multiply height and width
$\text{Exact Area} = \frac{11}{4} \times \frac{17}{2} = \frac{187}{8} = 23\frac{3}{8}$ square feet

Step5: Compare estimate and exact value

$23\frac{3}{8}$ is close to 27, so the estimate is 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: $\text{Total Area} = 2\frac{3}{4} \times 8\frac{1}{2}$; Exact Area = $23\frac{3}{8}$ square feet. The estimate of 27 is close to the exact value, so it is reasonable.