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. Bethany’s design would give the larger garden because the area would be 3,500 ft2. Tyler’s design would give the larger garden because the area would be 3,600 ft2. Bethany’s and Tyler’s designs would give a garden with the same area. Bethany’s and Tyler’s designs are not possible with the given amount of fencing.
we know that [perimeter of square]=4*a where a------> side length of a square so if Tyler and Bethany have 240 feet of fencing
Tyler’s design is a square 240=4*a-------> a=240/4-------> a=60 ft
[area of a square]=a²-----> 60²-----> 3600 ft² the area in Tyler’s design is 3600 ft²
Bethany’s design is a rectangle area of rectangle=length*width------> 50*70------> 3500 ft² perimeter of rectangle=2*[length +width]----> 2*[120]----> 240 ft
the answer is Tyler’s design would give the larger garden because the area would be 3,600 ft²
