SOLUTION: The length of a rectangle is 7 inches and the width is 4 inches. If both the length and width are increased by equal amounts, the area is increased by 42 square inches. Find the le
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Question 944289: The length of a rectangle is 7 inches and the width is 4 inches. If both the length and width are increased by equal amounts, the area is increased by 42 square inches. Find the length and width of the larger rectangle.
I am so confused!
Found 2 solutions by Theo, stanbon:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you start with a length of 7 and a width of 4.
the area is length * width which is equal to 7 * 4 = 28
when you increase the length and the width by the same amount, the area is increased by 42.
let the amount that you are increasing the length and width by be equal to x.
the new length is 4 + x.
the new width is 7 + x
since the original area is 28, and you increase it by 42, the new area must be equal to 70.
since length * width = area, you get:
(4 + x) * (7 + x) = 70
this can also be written as:
(x + 4) * (x + 7) = 70
multiply out the factors to get:
x^2 + 11x + 28 = 70
subtract 70 from both sides of the equation to get:
x^2 + 11x - 42 = 0
this is a quadratic equation that is in standard form.
factor it to get:
(x + 14) * (x - 3) = 0
solve for x to get x = -14 or x = 3
x can't be negative so the solution is x = 3
now go back to the original equation to see if you did this right.
with the original measurements, the area is equal to 7 * 4 = 28
when you add 3 to the length and you add 3 to the width, and you add 42 to the area, you get:
(7 + 3) * (4 + 3) = 28 + 42 which becomes 10 * 7 = 70 which becomes 70 = 70.
since this is a true statement, the value of 3 for x is confirmed as correct.
your answer is:
the length of the larger rectangle is 10.
the width of the larger rectangle is 7.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The length of a rectangle is 7 inches and the width is 4 inches. If both the length and width are increased by equal amounts, the area is increased by 42 square inches. Find the length and width of the larger rectangle.
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Area = length*width
Original Area = L*W
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Larger Area = (7+x)(4+x) = 7*4+42
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28+11x+x^2 = 28+42
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x^2 + 11x + 28 = 70
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x^2 + 11x - 42 = 0
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(x-3)(x+14) = 0
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Positive solution::
x = 3
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Ans:
length = 7+3 = 10
width = 4+3 = 7
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Cheers,
Stan H.
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