Question

A rectangular lawn is surrounded on three sides by flower beds. Each flowerbed is 2m wide. The area of the lawn is 14m(squared). What is the length of the lawn?



<---------------- 3x---------------------->
____________________________
|. | /|\
| 2m _____________________|. |
|<------> |. |. |
|. |. LAWN |. 2x
|. |____________________|. |
|. |. |
|____________________________|. \|/




My Workings:

3x - 2 ----------------->
__________________
|. |
|. 14m(squared) |. <------- 2x - 4
|. |
|_________________|

3x - 2 x 2x - 4 (?)


How would you do this?

Answer 1

(3x-2)(2x-4) = 14
6x^2-16x-6 = 0
2(x-3)(2x+1) = 0
x = 3

So the bed is 7x2

But you could have guessed that at first, since 2 and 7 are the only factors of 14...