Question

A rectangle has an area of 30m2. The width of the rectangle is 6m shorter than the length. Calculate these dimensions showing working out fully? Thank you

Answer 1

Your length is `3+sqrt39` and your width is `sqrt39-3`

Explanation:

Let x be the dimension of your length
Then `x-6` is the dimension of your width

To calculate the area of a rectangle, you have to multiply your width by your breadth
`x(x-6)=30`
`x^2-6x-30=0`

Using the quadratic formula,
`x=(-b+-sqrt(b^2-4ac))/(2a)`

`x=(6+-sqrt(36+120))/2`

`x=(6+-sqrt156)/2`

`x=(6+-2sqrt39)/2`

`x=3+-sqrt39`

Now, since your x is a dimension, it must be greater than 0
Hence, `x=3+sqrt39` only

therefore, your length is `3+sqrt39` and your width is `sqrt39-3`