SOLUTION: Please help me with this problem:The floor of a cabin is shaped like a rectangle. It has a surface area of 288 square feet. If the perimeter of the floor is 68 feet, what is the le

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Question 956109: Please help me with this problem:The floor of a cabin is shaped like a rectangle. It has a surface area of 288 square feet. If the perimeter of the floor is 68 feet, what is the length of the floor?
Found 2 solutions by Alan3354, macston:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Please help me with this problem:The floor of a cabin is shaped like a rectangle. It has a surface area of 288 square feet. If the perimeter of the floor is 68 feet, what is the length of the floor?
----------------
P = 2L + 2W = 68
L + W = 34
L*W = 288
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Find a pair of factors of 288 with a sum of 34.
---
1*288 NG
2*144 NG
3*96 NG
etc
Answer by macston(5194)   (Show Source): You can put this solution on YOUR website!
L=length;W=width; P=perimeter=68ft; A=area=288 sq ft
A=L*W
L=A/W
P=2(L+W) Substitute for L
68ft=2((A/W)+W) Divide each side by 2
34ft=(288sqft/W)+W Subtract W from each side.
34ft-W=288sqft/W Multiply each side by W
Subtract 288 from each side.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=4 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 16, 18. Here's your graph:

The width is 16ft or 18ft and length is the other.
ANSWER: The dimensions are 18 feet by 16 feet.
CHECK:
P=2(L+W)
68ft=2(18ft+16ft)
68ft=2(34ft)
68ft=68ft
A=LW
288 sq ft=(18ft)(16ft)
288 sq ft=288 sq ft
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