Question

1. Employees of a landscaping company built a retaining wall with area 23(3/8) sq ft. They used brick to make the top portion of the wall, which is 8(1/2) feet. What is the total height of the wall? Write an equation to represent the situation. Then solve. Part 2: If the area of the brick portion of the wall is 15(7/12), what fraction of the wall is brick? Write an equation to show your work.

Answer 1

Answer:

a. h = A/w = 2 ³/₄ ft

b. A'/A = 2/3

Step-by-step explanation:

a. What is the total height of the wall? Write an equation to represent the situation. Then solve.

The wall is a rectangle and its area is A = wh where w = width and h = height of wall.

Making h subject of the formula,

h = A/w

Now, Since the area of the retaining wall, A is 23 ³/₈ ft² and its width is the length of the portion of the wall which is brick w is 8 ¹/₂ ft, then

h = A/w

= 23 ³/₈ ft² ÷ 8 ¹/₂ ft

= 187/8 ft² ÷ 17/2 ft

= 187/8 ft² × 2/17 ft

= 187/4 ft² × 1/17 ft

= 187/68 ft

= 2 ³/₄ ft

b. If the area of the brick portion of the wall is 15(7/12), what fraction of the wall is brick? Write an equation to show your work.

Since the area of the brick portion of the wall is A' = 15 ⁷/₁₂ ft²  and the total are of the retaining wall is A =  23 ³/₈ ft²

The fraction of the wall that is brick = A'/A

= 15 ⁷/₁₂ ft² ÷ 23 ³/₈ ft²

= 187/12 ÷ 187/8

= 187/12 × 8/187

= 8/12

= 2/3