When 15m is added to two opposite sides of a square and 5m is added to the other sides, the area of the resulting rectangle is 441m^2. How do you find the length of the sides of the original square?

1 Answer
Alan P.
Feb 3, 2016

Length of original sides: sqrt(466)-10~~11.59 m.

Explanation:

Let s (meters) be the original length of the sides of the square.

We are told
color(white)("XXX")(s+5)xx(s+15) = 441

Therefore
color(white)("XXX")s^2+20s+75=441

color(white)("XXX")s^2+20x-366=0

Applying the quadratic formula: (-b+-sqrt(b^2-4ac))/(2a)
(with a bit of arithmetic)
we get:
color(white)("XXX")s=-10+-sqrt(466)

but since the length of a side must be >0
only s=-10+sqrt(466) is not extraneous.

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