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
