Jaqueline V.

asked • 07/13/15

Solving Word Problems with the quadratic formula

A rectangle has sides of length x feet and 2x+2 feet with an area of 24 square feet. Cassandra uses the quadratic formula and finds that x equals 3 and -4. She determines that this means the sides of the rectangle are -4 by -6 or 3 by 8. Why is she incorrect?

1 Expert Answer


Andrew M. answered • 07/13/15

Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors

David W.

Just a little bit more specifically, the values of -4 and -6 satisfy the quadratic equation x^2 + x -12 = 0, but they don't begin to fit the description of x feet and 2x + 2 feet, as Andrew M. said.  Remember, regardless of the process that we use to obtain the solution, all ansers must fit all of the original constraints (note:  you may also notice this with absolute value problems).


Andrew M.

-4 by -6 does fit  'x and 2x +2'
2(-4)+2 = -8
It also fits 24 ftsince (-4)(-6) = 24
The only reason she was wrong is that the length
and width of a rectangle cannot be a negative value.
Thus, while both 3 by 8 and -4 by -6 fit the
stated parameters, the only correct answer is
3 by 8


Andrew M.

Correction..., typo...,
so -4 by -6 does fit x and 2x+2


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