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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