Question

1. The length of Gordon Garden is 6 feet more than its width. A walkway 3 feet wide surrounds the outside of the garden. The total area of the garden and walkway is 720 square feet. Find the dimensions of the garden.

Answer 1

let x = width of garden so length = x + 6
total length including path = x + 6 + 2*3 = x + 12
.. width...................... = x + 2*3 = x + 6
total area = (x +6)(x+12) = 720
x^2 + 18x + 72 = 720
x^2 + 18x - 648 = 0

solve for x to get width and length

Answer 2

can you continue from here?

Answer 3

not really

Answer 4

ok - this omes not straight forward
you need 2 numbers whose product is -648 and whose sum is +18

you can find this from prime factors

18 = 2*3*3
648 =2*2*2*3*3*3*3
take out 2*3*3 out of factors of 648 leaves 2*2*3*3 = 36
- this gives 18 and 36
and +36 and -18 gives +18
- that gives factors of x^2 + 18x - 648:
(x - 18)(x + 36) = 0
x = 18 or -36 and as - 36 cannot be the width
width = 18
so length = 18 + 6 = 24

answer: dimensions of garden = 24 x 18