SOLUTION: 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

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!
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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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