Question

Quinn is building an enclosed pen in his backyard. He wants the perimeter to be no more than 50 feet. He also wants the length to be at least 5 feet longer than the width.

Which combination of width and length will meet Quinn’s requirements for the pen?

A.
width = 7 feet and length = 20 feet
B.
width = 5 feet and length = 12 feet
C.
width = 15 feet and length = 10 feet
D.
width = 11 feet and length = 15 feet

Answer 1

B

Explanation:

Answer 2

It would be B (width of 5 ft and length of 12 ft)

Explanation:

1) The only way to do this is by process of elimination. This means to use the requirements to take out answers that do not work.

2) First use the fact that the perimeter should not be more than 50.

• If we use this then the perimeter for each one. Perimeter= 2(L+W) for a rectangle with L being the Length and W being Width.
• For answer A (or figure A): 2(20+7)=2(27)= 2x27=54. A's Perimeter is larger than 50, which means it doesn't work.
• For B: 2(5+12)= 2(17)= 2x17= 34. B's perineter is lower than 50, making it work.
• For C: 2(15+10)= 2(25)= 50. C's perimeter is equal to 50, making it work as well.
• For D: 2(11+15)= 2(26)= 52. D's perimeter is more than 50, making it not work.

3) We are left with B and C as the possible answers. Now we use the second condition. The length must be 5 ft greater than the width. The only that works is B, since in C the width is greater than the length. In B, the length is greater than the width by more than 5.

Therefore B is your answer.