SOLUTION: A rectangle is drawn so that the width is 4 feet shorter than the length. The area of the rectangle is 12 square feet. Find the length of the rectangle.

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Question 861680: A rectangle is drawn so that the width is 4 feet shorter than the length. The area of the rectangle is 12 square feet. Find the length of the rectangle.
Found 2 solutions by ben720, josgarithmetic:
Answer by ben720(159) About Me  (Show Source):
You can put this solution on YOUR website!
A=12
lw=12
Because the width is 4 ft shorter,
l%28l-4%29=12
Distribute the l
l%5E2-4l=12
Subtract 12 from both sides
l%5E2-4l-12=0
Use the quadratic formula
l+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
l+=+%284+%2B-+sqrt%28+-4%5E2-4%2A1%2A-12+%29%29%2F%282%2A1%29+
l+=+%284+%2B-+sqrt%2816%2B48%29%29%2F%282%29+
l=%284%2B-sqrt%2864%29%29%2F2
l=%284%2B8%29%2F2ORl=%284-8%29%2F2
l=12%2F2ORl=-4%2F2
l=6ORl=-2
Because the length can't be negative, l=6. Because the width is 4 less, it's 2.

The length is 6 feet

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Common enough to be worth generalizing.
width w, length L.
Width is soe k feet shorter than length, or w=L-k.
Area is given, and may be called A.
The unknown variables are L and w.
(A=12 and k=4).

wL=A
%28L-k%29L=A
L%5E2-kL-A=0
-
Note that your given values for area and for k may render the quadratic equation in L as factorable. In GENERAL, you cannot rely on factorizability.
General Solution to Quadratic Equation gives for L,
L=%28k%2Bsqrt%28k%5E2-4%28-A%29%29%29%2F2
highlight%28highlight_green%28L=%28k%2Bsqrt%28k%5E2%2B4A%29%29%2F2%29%29.

You can substitute the values for A and k to compute L.