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?

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

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