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. which plan would cost less in fencing? explain design 1 design 2 1,296 ft² 36 ft 15 ft

Explanation:

Step1: Find the side length of the square in Design 1

The area of a square is \(A = s^{2}\), where \(A = 1296\) square feet. So, \(s=\sqrt{1296}=36\) feet.

Step2: Calculate the perimeter of Design 1

The perimeter of a square is \(P = 4s\). Substituting \(s = 36\), we get \(P_1=4\times36 = 144\) feet.

Step3: Calculate the perimeter of Design 2

The perimeter of Design 2 has two lengths of \(36\) feet and three widths of \(15\) feet. So \(P_2=(2\times36)+(3\times15)=72 + 45=117\) feet. But wait, no, correct formula: For Design 2, the total fencing is \(2\times(15 + 36)+36\). First, \(15+36 = 51\), then \(2\times51=102\), and \(102 + 36=138\) feet.

Step4: Find the difference in perimeters

\(\Delta P=P_1 - P_2\). \(P_1 = 144\) and \(P_2=132\) (corrected calculation: For Design 1: \(A = s^{2}=1296\), \(s = 36\), \(P_1=4\times36=144\). For Design 2: two rectangles, total fencing: \(2\times(36 + 15)+36\) (the dividing line). \(2\times51+36=102 + 36=132\). \(\Delta P=144-132 = 12\)

Answer:

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