Question

Holly has a rectangular garden that measures 12 m wide by 14 m long. She wants to increase the area to 255 m² by increasing the width and length by the same amount.
What will be the length (longer dimension) of the new garden?

Answer 1

X is increase
(12+x) times (14+x)=255
expand
x²+26x+168=255
minus 255 both sides
x²+26x-87=0
factor
what 2 numbers multiply to get -87 and add to get 26?
-3 and 29
(x-3)(x+29)=0
set each to zero

x-3=0
x=3

x+29=0
x=-29
false, if we increased each by -29, then we would get negative measures
get rid of this solution
x=3

the new length is 3+14 or 17m

Answer 2

Present area = 12 * 14 = 168 square meters
The area has to increase by a factor of 255 / 168 = 1.5178571429
Therefore, the width and length are increased by a factor of the
square root of 1.5178571429 = 1.2320134508

So the width becomes
12 * 1.2320134508 =  14.7841614091
and the length becomes
14 * 1.2320134508 =  17.2481883107

That's roughly 14.78 by 17.25 and the area equals
14.78 * 17.25 = 255 square meters