Question

rashad is considering two designs for a garden. in design 1 he would use fencing to surround a square plot of land that has an area of 1,296 square feet. in design 2 he would divide a plot of land into two rectangular sections, each 15 feet by 36 feet, and surround the plot with fencing, as well as place fencing along the dividing line of the two sections. design 1 (square with area 1,296 ft²) design 2 (two rectangles, each 15 ft by 36 ft, with a dividing fence) which plan would cost less in fencing? explain. option 1: design 1, because it requires 12 fewer feet of fencing than design 2 option 2: design 1, because it requires 24 fewer feet of fencing than design 2 option 3: design 2, because it requires 12 fewer feet of fencing than design 1 option 4: design 2, because it requires 24 fewer feet of fencing than design 1

Explanation:

Step1: Find side length of Design1

The area of a square is $A = s^2$. For $A=1296$, solve for $s$:
$$s = \sqrt{1296} = 36 \text{ feet}$$

Step2: Calculate fencing for Design1

Perimeter of square: $P = 4s$
$$P_1 = 4 \times 36 = 144 \text{ feet}$$

Step3: Calculate fencing for Design2

First, find total outer dimensions: combined width is $15+15=30$ ft, height 36 ft. Outer perimeter is $2(30+36)$. Add the 36 ft dividing fence:
$$P_2 = 2(30+36) + 36 = 2(66) + 36 = 132 + 36 = 168 \text{ feet}$$

Step4: Find difference in fencing

$$P_2 - P_1 = 168 - 144 = 24 \text{ feet}$$

Answer:

Design 1, because it requires 24 fewer feet of fencing than Design 2