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. 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.

Answer 1

Tyler’s design would give the larger garden because the area would be 3,600 ft2.

Explanation:

the area of bethany's is 70*50 = 3500

the area of tyler's is 240/4 = 60, 60*60= 3600

so tyler's is larger than bethany's

Answer 2

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