Question

tyler and bethany have 240 feet of fencing with which to build a garden. tyler wants the garden to be in the shape of a square, while bethany wants it to be rectangular with a length of 50 feet and a width of 70 feet. which design would give the maximum area for the garden? explain.
bethanys design would give the larger garden because the area would be 3,500 ft²
tylers design would give the larger garden because the area would be 3,600 ft²
bethanys and tylers designs would give a garden with the same area
bethanys and tylers designs are not possible with the given amount of fencing

Explanation:

Step1: Calculate the side length of Tyler's square

The perimeter of a square is \(P = 4s\), where \(P = 240\) feet. So, \(s=\frac{P}{4}\).
\(s=\frac{240}{4}=60\) feet.

Step2: Calculate the area of Tyler's square

The area of a square is \(A = s^{2}\).
\(A=(60)^{2}=3600\) \(ft^{2}\).

Step3: Calculate the area of Bethany's rectangle

The area of a rectangle is \(A = l\times w\), where \(l = 50\) feet and \(w = 70\) feet.
\(A=50\times70 = 3500\) \(ft^{2}\).

Answer:

Tyler’s design would give the larger garden because the area would be \(3600\) \(ft^{2}\).