Question 1126554: The length of a warehouse is 23 ft more than its width. Find the width and length of the warehouse if its area is 6840 ft^2
How do you find length and width of a rectangle when given the area?
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52786)   (Show Source):
You can put this solution on YOUR website! .
Let W represents the width, in feet.
Then the length is (W+23) feet, and the equation for the area is
W*(W+23) = 6840.
It gives you the quadratic equation
W^2 + 23W - 6840 = 0.
Solve it by using the quadratic formula to find W.
That's all.
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Let me give you an advise about using factoring when solving quadratic equations.
If you can not find the factoring mentally in your head in 5 - 10 seconds - USE THE QUADRATIC FORMULA.
In this case, I DEFINITELY advise you to use the quadratic formula.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! area of a rectangle is length * width.
let L = length and let W = width.
area of a rectangle becomes L * W.
if the length is 23 feet more than the width, then L = W + 23.
replace L with W + 23 in the formula and you get area of a rectangle = (W + 23) * W.
simplify to get area of the rectangle = 23W + W^2
since the area is 6840, then the formula becomes 6840 = 23W + W^2
subtract 6840 from both sides of the equation and re-order the terms in descending order of degree and flip sides to get:
W^2 + 23W - 6840 = 0
factor this quadratic equation to get:
(W+95) * (W-72) = 0
solve for W to get W = -95 or W = 72.
W can't be negative, so W = 72.
since L = W + 23, then L = 95
length is 95 and width is 72
area is length * width = 95 * 72 = 6840.
length is 23 greater than width.
solution looks good.
solution is length = 95 and width = 72.
even though the quadratic was factor-able, if it wasn't obvious what the factors needed to be, then use the quadratic formula to find the answer.
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