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Question

Difficulty: MediumPerimeter and Area of 2D Figures

A rectangular landing pad is designed so that its length is exactly three times its width. If the total area of the landing pad is 147147 square meters, what is the perimeter of the landing pad in meters?

Answer: 56 meters

Answer

56
By setting the width as ww and length as 3w3w, the area equation is 3w2=1473w^2 = 147. Solving for ww yields a width of 77 meters, making the length 2121 meters. The perimeter is the sum of all four sides: 2(21+7)=562(21 + 7) = 56 meters.

Step-by-Step Solution

1
Define variables and set up the area equation.
w×3w=147w \times 3w = 147
The area of a rectangle is width times length, and the length is given as three times the width.
2
Solve for the width (ww).
w2=49⇒w=7w^2 = 49 \Rightarrow w = 7
Dividing both sides by 33 isolates w2w^2, and taking the square root gives the width.
3
Calculate the length and the perimeter.
Length = 2121, Perimeter = 5656
Length is 3×73 \times 7. Perimeter is 2(21+7)2(21 + 7).

Key Concept

Calculating the perimeter of a rectangle when given its area and the proportional relationship between its sides.
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Topics

Perimeter and Area of 2D Figures

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