Question

The area of a rectangular floor is described by the equation w(w-9)=252 where w is the width of the floor in meters. What is the width o the floor?

Answer 1

Width `(w) = 21`

Explanation:

Given:
`w(w-9)=252`

Multiply everything inside the brackets by `w`

`=>w^2-9w=252`

Subtract 252 from both sides

`w^2-9w-252=0`

Factors of 252 that have a difference of 9 are 12 and 21
We need -9 so the larger if the two is negative.

`(w-21)(w+12) =w^2+12w-21w-252color(red)(" Works")`

So
`w-21=0" " =>" " w=+21`
`w+12=0" "=>" "w=-12 color(red)(larr" negative value not logical")`

Width `(w) = 21`