Question

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?

Answer 1

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.