Question

the area of a rectangle is x^2+3x-4 the width of the rectangle is x-1. determine the ratio of the area to the width

Answer 1

The ratio of the area to the width is equal to
`(x+4)\ units`

Explanation:

we know that

`A=x^(2) +3x-4`

Completing the square

`x^(2) +3x=4`

`(x^(2) +3x+(9/4))=4+(9/4)`

`(x^(2) +3x+(9/4))=25/4`

`(x+(3/2))^(2)=25/4`

`(x+(3/2))=(+/-)5/2`

`x=-(3/2)(+/-)5/2`

`x=-(3/2)(+)5/2=1`

`x=-(3/2)(-)5/2=-4`

therefore

`x^(2) +3x-4=(x-1)(x+4)`

Find the ratio of the area to the width

`(A)/(W)=((x-1)(x+4))/(x-1)=(x+4)\ units`