rashad is considering two designs for a garden. in design 1 he would use fencing to surround a square plot…

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. which plan would cost less in fencing? explain. design 1, because it requires 12 fewer feet of fencing than design 2 design 1, because it requires 24 fewer feet of fencing than design 2 design 2, because it requires 12 fewer feet of fencing than design 1 design 2, because it requires 24 fewer feet of fencing than design 1

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. which plan would cost less in fencing? explain. design 1, because it requires 12 fewer feet of fencing than design 2 design 1, because it requires 24 fewer feet of fencing than design 2 design 2, because it requires 12 fewer feet of fencing than design 1 design 2, because it requires 24 fewer feet of fencing than design 1

Answer

Answer:

A. Design 1, because it requires 12 fewer feet of fencing than Design 2

Explanation:

Step1: Find side - length of square in Design 1

Let the side - length of the square be $s$. Given $A = s^{2}=1296$, then $s=\sqrt{1296}=36$ feet. The perimeter of the square $P_1 = 4s=4\times36 = 144$ feet.

Step2: Calculate perimeter of Design 2

The combined rectangle in Design 2 has length $l = 36$ feet and width $w=15 + 15=30$ feet. The perimeter of the outer rectangle is $2(l + w)=2(36+30)=132$ feet, and we add the internal dividing line of length 36 feet. So $P_2=132 + 36=156$ feet.

Step3: Compare perimeters

Find the difference $\Delta P=P_2 - P_1=156-144 = 12$ feet. Design 1 has a smaller perimeter, so it requires 12 fewer feet of fencing.