Jose just removed the children's playset from his back yard to make room for a rectangular garden. He wants to put a fence around the garden to keep out the dog. He has a 90 foot roll of fence in his garage that he plans to use. To fit in the backyard, the width of the garden must be 15 feet. How long can he make the other side, in feet, if he wants to use the entire roll of fence?

Explanation:

He has 90 feet of fencing overall. This is the perimeter of the rectangle as its the distance around all four sides.

Two of the opposite sides are the width = 15 ft. So we have 15+15 = 30 feet taken up and 90-30 = 60 feet left for the other two opposite sides to add to. Call each of those sides x

x+x = 60

2x = 60

x = 60/2

x = 30

The other side must be 30 feet long.

This rectangle is 30 by 15

perimeter = 30+15+30+15 = 45 + 45 = 90

which helps confirm we have the right answer

Or you can solve this way

P = 2*(L+W) is the perimeter of a rectangle with length L and width W

Plug in the perimeter P = 90 and the width W = 15. Solve for L

P = 2*(L+W)

90 = 2*(L+15)

2(L+15) = 90

L+15 = 90/2

L+15 = 45

L = 45-15

L = 30

each side has a different length.  

step-by-step explanation: