SOLUTION: The area of a rectangle is 154 sq. Ft. If its width is 3 ft. less than its length what are its dimensions? I need to use a quadratic formula to solve it. ty

Algebra ->  Rectangles -> SOLUTION: The area of a rectangle is 154 sq. Ft. If its width is 3 ft. less than its length what are its dimensions? I need to use a quadratic formula to solve it. ty       Log On


   

Question 129109: The area of a rectangle is 154 sq. Ft. If its width is 3 ft. less than its length what are its dimensions? I need to use a quadratic formula to solve it.
ty
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the formula for the area of a rectangle:
A+=+L%2AW
You are told that the width, W is 3 ft. less than the length, L, so this can be written as:
W+=+L-3 so now you can replace W with (L-3) and write:
A+=+L%2A%28L-3%29 and you are also told that the area is 154 sq.ft., so...
L%2A%28L-3%29+=+154 Simplify.
L%5E2-3L+=+154 Subtract 154 from both sides.
L%5E2-3L-154+=+0 There's your quadratic equation and it can be solve by factoring.
%28L-14%29%28L%2B11%29+=+0 Applying the zero products principle, we get:
L-14+=+0 or L%2B11+=+0 so that...
L+=+14 or L+=+-11 Use only the positive value as lengths are positive quantities.
L+=+14 and...
W+=+L-3
W+=+14-3
W+=+11
The dimensions of the rectangle are:
Length = 14 ft. and width = 11 ft.
Check:
A+=+L%2AW
A+=+14%2A11
A+=+154sq.ft.