Question

The length of a rectangle is 3 centimeters less than its width. What are the dimensions of the rectangle if its area is 54 square​ centimeters?

Answer 1

Width`=9cm`
Length`=6cm`

Explanation:

Let `x` be width, then length is `x-3`
Let area be `E`. Then we have:
`E=x*(x-3)`
`54=x^2-3x`
`x^2-3x-54=0`

We then do the Discriminant of the equation:

`D= 9+216`
`D=225`

`X_1 = (3 + 15)/2 = 9`
`X_2 = (3-15)/2 = -6` Which is declined, since we can't have negative width and length.

So `x=9`
So width `= x = 9cm` and length`=x-3=9-3=6cm`

Answer 2

Length is `6cm` and the width is `9cm`

Explanation:

In this question, the length is less than the width. It does not matter at all - they are just names for the sides. Usually the length is longer, but let's go with the question.

Let the width be `x`
The length will be `x-3" "` ( it is `3`cm less)

The area is found from `l xx w`

`A = x(x-3) =54`

`x^2-3x -54 =0" "larr` make a quadratic equation equal to `0`

Factorise: Find factors of `54` which differ by `3`

`(x" "9)(x" "6)=0`

There must be more negatives: `" "` because of `-3x`

`(x-9)(x+6)=0`

Solve for `x`

`x-9=0" "rarr x =9`

`x+3=0" "rarr x =-3" "` reject as the length of a side.

the width is `9cm` and the length is `9-3 =6cm`