Question

which amount of 1 inch square pieces of chocolate would you rather have and why? A. Enough to cover a rectangle with a length of 9 in. and a perimeter of 22 in. B. Enough to cover a rectangle with a length of 5 in. and a perimeter of 20 in.

Answer 1

I'd rather pick the option B since the rectangle has a larger area and therefore I'd have more 1 inch square pieces of chocolate.

Explanation:

The perimeter of a rectangle is given by:

p = 2*width + 2*length

For the first rectangle the perimeter is 22 in and the length is 9, so the width is:

22 = 2*9+2*width

2*width+18=22

2*width=4

width = 2

Then the area of the rectangle is:

a = width*length=2*9 = 18 square inches

Choosing this option gives us 18 pieces of chocolate.

For the second rectangle the perimeter is 20 and the length is 5, so the width is:

20 = 2*5 + 2*width

2*width + 10 = 20

2*width = 20-10

2*width = 10

width = 5

So the area is:

a = 5*5 = 25 square inches

Choosing this option gives us 25 pieces of chocolate.

I'd rather pick the option B since the rectangle has a larger area and therefore I'd have more 1 inch square pieces of chocolate.