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?
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!
its 17
To determine the width of the border, we need to find the area covered by the brick walkway.
Let's start by calculating the area of the rectangular garden. The garden measures 6 meters by 15 meters, so the area is given by multiplying the length by the width:
Area of garden = Length × Width = 6 meters × 15 meters = 90 square meters
Now, we need to consider the brick walkway, which will run along the length of the garden, turn the corner, and run along the width. We know that the area covered by the walkway is 46 square meters.
Area of walkway = 46 square meters
To find the width of the border, we subtract the area of the walkway from the total area of the garden:
Width of border = Area of garden - Area of walkway
Width of border = 90 square meters - 46 square meters
Width of border = 44 square meters
Therefore, the border should have a width of 44 meters to allow for the brick walkway.