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If
the length of a rectangle is reduced by 3 meters and the
width is increased by 2 meters, the result is a square
whose area is the same as that of the rectangle. What
is that area?

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METHOD
1: Make a chart
In the table shown at right, after values are assigned
to the sidelength of the square, the rectangle's
corresponding dimensions are computed and then the
areas of both figures. The area, 36
sq m, is the number common to the last
two columns.


METHOD
2: Use algebra
If x is the sidelength of the square, then the
dimensions of the rectangle are x + 3 and x  2.
Their areas, respectively are x^2 and (x + 3)(x  2). Thus x^2
= (x + 3)(x  2). This becomes x^2 = x^2 + x  6,
which simplifies to x  6 = 0.
So, x = 6 and the area is 36 sq m.

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