SOLUTION: I saw this problem in my textbook: A rectangle has a perimeter of 42 miles and an area of 104 square miles. Find the dimensions of the rectangle. My question is... how do you

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I saw this problem in my textbook: A rectangle has a perimeter of 42 miles and an area of 104 square miles. Find the dimensions of the rectangle. My question is... how do you       Log On


   

Question 327379: I saw this problem in my textbook:
A rectangle has a perimeter of 42 miles and an area of 104 square miles. Find the dimensions of the rectangle.
My question is... how do you get the answer? I've tried making two equations and solving for one variable, but it didn't work.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for perimeter of a rectangle is,
P=2%2AL%2B2%2AW=42
1.L%2BW=21
The formula for area of a rectangle is,
A=L%2AW=104
2.L%2AW=104
From eq. 1,
L=21-W
Substitute into eq. 2,
%2821-W%29W=104
21W-W%5E2=104%7D%7D%5D%0D%0A%7B%7B%7BW%5E2-21W%2B104=0
You can factor this quadratic,
%28W-13%29%28W-8%29=0
Two solutions:
W-13=0
W=13 Then from above,
L%2B13=21
L=8
.
.
.
W-8=0
W=8
L=13
.
.
.
The rectangle is 13 miles by 8 miles.