SOLUTION: I need to come up with an equation (I am in algebra) and then compute the following: The length of a rectangular table top is 8 feet shorter than 5 times the width. If the area

Algebra ->  Formulas -> SOLUTION: I need to come up with an equation (I am in algebra) and then compute the following: The length of a rectangular table top is 8 feet shorter than 5 times the width. If the area      Log On


   

Question 21574: I need to come up with an equation (I am in algebra) and then compute the following:
The length of a rectangular table top is 8 feet shorter than 5 times the width. If the area of the table top is 48 square feet, find the dimensions of the table? I am so confused. Can someone help!!
Found 2 solutions by Paul, Earlsdon:
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Look under problem NO. 10320 it is already solved

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the length of the table top be L and its width W.
L = 5W-8
The area of a rectangle is:
A+=+L%2AW Substitute L = 5W-8
A+=+%285W-8%29%28W%29
A+=+5W%5E2-8W But A = 48 sq.ft.
48+=+5W%5E2-8W Subtract 48 from both sides.
5W%5E2-8W-48+=+0 Solve by factoring.
%285W%2B12%29%28W-4%29+=+0 Apply the zero product principle.
%285W%2B12%29+=+0 and/or W-4%29+=+0
If 5W%2B12+=+0%7D%7D+then%2C+5W+=+-12 and W+=+-12%2F5 Discard this solution as the width can only be positive.
If W-4+=+0 then, W+=+4
The width is 4 feet.
The length, L, is 5(4)-8 = 20 - 8 = 12 feet.
Check:
A = L*W
A = 12*4
A = 48 sq.ft.