Henry and Liani have 200 feet of wood to frame a flower bed. Henry wants the bed to be a square, while Liani wants it to be a rectangle with dimensions of 55 feet and 45 feet. Which statement is true regarding the areas of the two flower beds?

A. Henry's design would result in a larger flower bed because its area would be 2,500 square feet.

B. Liani's design would result in a larger flower bed because its area would be 2,500 square feet.

C. Henry's and Liani's designs would result in flower beds with the same area. D. Henry's and Liani's designs are not possible with the given amount of wood.

Question

Mathematics

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31 May, 20:35

Henry and Liani have 200 feet of wood to frame a flower bed. Henry wants the bed to be a square, while Liani wants it to be a rectangle with dimensions of 55 feet and 45 feet. Which statement is true regarding the areas of the two flower beds?

A. Henry's design would result in a larger flower bed because its area would be 2,500 square feet.

B. Liani's design would result in a larger flower bed because its area would be 2,500 square feet.

C. Henry's and Liani's designs would result in flower beds with the same area. D. Henry's and Liani's designs are not possible with the given amount of wood.

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Answers (1)

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Tia Bradley · Answer 1

Henry's design would result in a larger flower bed because its area would be 2500 square feet.

Henry : perimeter (P) = 4a ... where a is one side of the square ...

200 = 4a

200/4 = a

50 = a ... so each side of the square is 50 ft.

Area of a square (A) = a^2 ... where a is one side of the square ...

A = 50^2 = 2500 ft^2

Liani : Area of rectangle (A) = length x width

A = L * W

A = 55 * 45

A = 2475 ft^2

so u can see that Henry's design would have a larger area then Liani's