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Difficulty: MediumPerimeter and Area of 2D Figures

A landscaping company is designing a parallelogram-shaped flower bed that will cover exactly 288288 square feet. If the design requires the base of the flower bed to be twice its height, what must the length of the base be in feet?

Answer: 24 ft

Answer

24
The area of a parallelogram is the product of its base and height (A=b×hA = b \times h). By substituting 2h2h for the base, the equation becomes 288=2h2288 = 2h^2. Solving for hh yields 1212. The base is twice the height, so 2×12=242 \times 12 = 24.

Step-by-Step Solution

1
Set up the area formula
A=b×hA = b \times h
To relate the given area to the dimensions of the parallelogram.
2
Express the base in terms of height
b=2hb = 2h
The problem states the base is twice the height.
3
Substitute the expressions into the area equation
288=(2h)×h288 = (2h) \times h
To create an equation with only one variable.
4
Solve for the height (hh)
2h2=288⇒h2=144⇒h=122h^2 = 288 \Rightarrow h^2 = 144 \Rightarrow h = 12
To find the numerical value of the height.
5
Calculate the base (bb)
b=2×12=24b = 2 \times 12 = 24
The question asks for the length of the base, not the height.

Key Concept

Area of a parallelogram and algebraic substitution
Estimated Time:1m 0s
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Topics

Perimeter and Area of 2D Figures

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