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?

Feb 3, 2016

Length of original sides: $\sqrt{466} - 10 \approx 11.59$ m.

Explanation:

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

We are told
$\textcolor{w h i t e}{\text{XXX}} \left(s + 5\right) \times \left(s + 15\right) = 441$

Therefore
$\textcolor{w h i t e}{\text{XXX}} {s}^{2} + 20 s + 75 = 441$

$\textcolor{w h i t e}{\text{XXX}} {s}^{2} + 20 x - 366 = 0$

Applying the quadratic formula: $\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
(with a bit of arithmetic)
we get:
$\textcolor{w h i t e}{\text{XXX}} s = - 10 \pm \sqrt{466}$

but since the length of a side must be $> 0$
only $s = - 10 + \sqrt{466}$ is not extraneous.