Question

The length of a rectangle is 3cm more than its width and it has an area of 230 square cm. How do you find the width to 1 decimal place?

Answer 1

`13.7` `"cm"`

Explanation:

The rectangle's length can be written in terms of its relation to the width as follows:

`l=w+3`

Thus, if `A=lw`,

`A=(w+3)w`

`A=w^2+3w`

We also know that the area of the rectangle is `230`, so

`230=w^2+3w`

This is a quadratic equation.

`0=w^2+3w-230`

Use the quadratic formula:

`w=(-3+-sqrt(3^2-4(1)(-230)))/(2(1))`

`w=(-3+-sqrt929)/2`

`w=13.7,color(red)(cancel(color(black)(-16.7`

Eliminate the negative answer since width cannot be negative.