Question

a farmer wants to build a garden using fence. a total of 60 feet of fence will be used to enclose the garden. the farmer calculates that the area of the garden will be 225 square feet if a square - shaped garden is built using the fence. the farmer also considers building the garden in different shapes to increase the area enclosed by the fence. determine how building the garden in different shapes affects the area of the garden. select the boxes to compare the area of the gardens. select only one box per row. shape of the garden less than 225 square feet equal to 225 square feet greater than 225 square feet equilateral triangle rectangle with dimensions 18 feet by feet

Explanation:

Step1: Calculate area of equilateral triangle

Let the side - length of the equilateral triangle be $s$. The perimeter $P = 3s$. Given $P=60$ feet, then $s = 20$ feet. The area formula for an equilateral triangle is $A=\frac{\sqrt{3}}{4}s^{2}$. Substituting $s = 20$ into the formula, we get $A=\frac{\sqrt{3}}{4}\times20^{2}=\frac{\sqrt{3}}{4}\times400 = 100\sqrt{3}\approx173.2$ square feet. Since $173.2<225$, the area of the equilateral - triangle - shaped garden is less than 225 square feet.

Step2: Calculate area of rectangle

The dimensions of the rectangle are 18 feet by $l$ feet. The perimeter $P = 2(18 + l)$. Since $P = 60$ feet, we have $2(18 + l)=60$. First, divide both sides by 2: $18 + l=30$. Then solve for $l$: $l = 12$ feet. The area of the rectangle $A=18\times12 = 216$ square feet. Since $216<225$, the area of the rectangle - shaped garden is less than 225 square feet.

Answer:

Equilateral triangle: Less than 225 square feet
Rectangle with dimensions 18 feet by 12 feet: Less than 225 square feet