Question

A field measuring 12 meters by 16 meters is to have a brick paver walkway installed all around it, increasing the total area to 285 square meters. How wide will the walkway be?

Answer 1

The walkway would be 1.5 meters wide.

Explanation:

First, we should calculate the total area of the field before adding the walkway, which is the product of its sides:

`12 m*16 m=192 m^2`

So the total area before installing the walkwayt is 192 square meters. Adding the walkway increase it to 285 square meters, so the area occupied by the walkway is the difference between those two values:

`285 m^2-192m^2=93m^2`

That gives an area of 93 square meters. We'll call this area A. We can calculate A by adding the area inreace on each side and the area increase on the corners. We already have the length of each side, so the area increace on each one is its value times the walkway width w, and the added area on the corners is w times w. Since we have two sides with length 12 meters, two sides with length 16 meters and four corners:

`A=2*16*w+2*12*w+4*w*w\\A=32w+24w+4w^2\\A=56w+4w^2`

We already calculated the value of A, so replacing and rearranging we get:

`93=56w+4w^2\\4w^2+56w-93=0`

This is a second degree equation, which is solved using the equations:

`w_(1) =(-56+√(56^2-4*4*(-93)))/(2*4)\\w_(1) =1.5\\w_(2) =(-56-√(56^2-4*4*(-93)))/(2*4)\\w_(2) =-15.5`

Since w can't be a negative quantity, we discard that value and get that the walkway width is 1.5 meters.