Question 824759: The width of a rectangle is 2 cm less than a side of a square, and the length is 1 cm more than a side of a square. If the area of the rectangle is 28 cm^2, find the length of a side of the square.
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
x = side of square
y = length of rect
z = width of rect
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z = x - 2
y = x + 1
yz = 28
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z = 28/y
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z = x - 2
z = 28/y
x - 2 = 28/y
y(x - 2) = 28
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y(x - 2) = 28
y = x + 1
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(x + 1)(x - 2) = 28
xx - x - 2 = 28
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xx - x - 30 = 0
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the above quadratic equation is in standard form, with a=1, b=-1, and c=-30
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
1 -1 -30
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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this quadratic has two real roots (the x-intercepts), which are:
x = 6
x = -5
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the negative root does not fit the problem statement, so use the positive root
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answer:
x = side of square = 6 cm
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