Question

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? henrys design would result in a larger flower bed because its area would be 2,500 square feet lianis design would result in a larger flower bed because its area would be 2,500 square feet henrys and lianis designs would result in flower beds with the same area henrys and lianis designs are not possible with the given amount of wood

Explanation:

Step1: Calculate side - length of Henry's square

The perimeter of a square is $P = 4s$, where $P$ is the perimeter and $s$ is the side - length. Given $P=200$ feet, then $s=\frac{P}{4}=\frac{200}{4} = 50$ feet.

Step2: Calculate area of Henry's square

The area of a square is $A_{1}=s^{2}$. Substituting $s = 50$ feet, we get $A_{1}=50^{2}=2500$ square feet.

Step3: Calculate area of Liani's rectangle

The area of a rectangle is $A_{2}=l\times w$, where $l = 55$ feet and $w = 45$ feet. So $A_{2}=55\times45=2475$ square feet.

Answer:

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