Question 821654: a rectangle is 3cm longer than it is wide. the diagonal is 15 cm. find the dimensions of the rectangle. use quadratic formula Found 2 solutions by stanbon, TimothyLamb:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! a rectangle is 3cm longer than it is wide. the diagonal is 15 cm. find the dimensions of the rectangle. use quadratic formula
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width = x cm
length = x+3 cm
diag = 15 cm
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Use Pythgoras:
x^2 + (x+3)^2 = 15^2
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x^2 + x^2 + 6x + 9 = 225
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2x^2 + 6x - 216 = 0
x^2 + 3x - 108 = 0
(x-9)(x+12) = 0
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Positive solution:
x = 9 cm (width)
x+3 = 12 cm (width)
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Cheers,
Stan H.
You can put this solution on YOUR website! ---
x = y + 3
15 = sqrt( xx + yy )
225 = xx + yy
225 = (y + 3)(y + 3) + yy
225 = yy + 6y + 9 + yy
2yy + 6y - 216 = 0
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the above quadratic equation is in standard form, with a=2, b=6, and c=-216
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
2 6 -216
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the two real roots (i.e. the two x-intercepts), of the quadratic are:
y = 9
y = -12
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negative width doesn't make sense so use the positive root:
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answer:
w= 9 cm
L= 12 cm
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