SOLUTION: Thank you for helping me. I am having problems with 2 problems: 1. The length of a rectangle is five times the width. The perimeter is 84 feet. What is the length & width of t

Algebra ->  Equations -> SOLUTION: Thank you for helping me. I am having problems with 2 problems: 1. The length of a rectangle is five times the width. The perimeter is 84 feet. What is the length & width of t      Log On


   

Question 665268: Thank you for helping me. I am having problems with 2 problems:
1. The length of a rectangle is five times the width. The perimeter is 84 feet. What is the length & width of the rectangle?
2. The width of a rectangle is 9cm less than twice the length. The perimeter is 72 cm. What is the length & width of the rectangle?
Thank you,
Scott
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
1)...
Given
l = 5w
p = 84 = 2l+2w
Substitute l into the equation for p
...
2(5w)+2w=84
Distribute the2
10w + 2w = 84
Combine like terms
12w = 84
Divide both sides by 12
w = 7 is the width
l = 5(7) = 35 is the length
...
Check
2(7) + 2(35) = 14 + 70 = 84
....
2)...
Given
w = 2l - 9
p = 72 = 2l+2w
Substitute w into the equation for p
...
2l + 2(2l-9) = 72
Distribute the 2
2l + 4l - 18 = 72
Isolate l
6l = 72 + 18
6l = 90
Divide both sides by 6
l = 15 is the length
w = 2(15)-9 = 21 is the width
...
check
2(21) + 2(15) = 42 + 30 = 72
....................
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