Question

You are putting a brick walkway along two sides of a rectangular garden that measures 6 meters by 15 meters.
The path will run the length of the garden, turn the corner, and run along the width.
You only have enough brick to cover 46 square meters. How wide should the border be?

Answer 1

let the width of the walkway be x m

area of walkway
= (6+2x)(15+2x) - (6)(15) = 46

90 + 42x + 4x^2 - 90 = 46
4x^2 + 42x - 46 = 0
2x^2 + 21x - 23 = 0
(x-1)(2x + 23) = 0
x = 1 or x = -23 which would be inadmissable

The border should be 1 m wide

check:
area of garden = 6x15 = 90
area including the border
= 8 x 17 = 136
and..... 136-90 = 46 ,
all is good!

Answer 2

its 17