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Algebra/Algebraic Equation

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Expert: - 12/31/2009


Question
The area of a rectangle is 48cm^2. If its length is increased by 1cm and its breadth is decreased by 1cm, it becomes a square. Find the dimensions of the rectangle. Solve using algebraic equation only.

Answer
Hello Miharu,

Let L=the length of the rectangle, W=the width.
We have LW=48, and L+1=W-1, since a square has all sides
of equal length.  Thus, L=W-2...substitute that into LW=48
to get: (W-2)W=48 ==> W^2-2W-48=0 ==> (W-8)(W+6)=48
==> W=8 or -6, since W cannot be negative, W=8 cm, and L=6 cm

OK?

Happy New year!

Abe

Algebra

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Volunteer

Abe Mantell

Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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