Question

The width of a rectangle is 3 inches less than its length. The area of the rectangle is 340 square inches. What are the length and width of the rectangle?

Answer 1

Length and width are 20 and 17 inches, respectively.

Explanation:

First of all, let us consider `x` the length of the rectangle, and `y` its width. According to the initial statement:

`y = x-3`

Now, we know that the area of the rectangle is given by:

`A = x cdot y = x cdot (x-3) = x^2-3x`

and it is equal to:

`A = x^2-3x=340`

So we get the quadratic equation:

`x^2-3x-340=0`

Let us solve it:

`x = {-b pm sqrt{b^2-4ac}}/{2a}`

where `a, b, c` come from `ax^2+bx+c=0`. By substituting:

`x = {-(-3) pm sqrt{(-3)^2-4 cdot 1 cdot (-340)}}/{2 cdot 1} =`
`={3 pm sqrt{1369}}/{2} = {3 pm 37}/2`

We get two solutions:

`x_1 = {3 + 37}/2 = 20`
`x_2 = {3-37}/2 = -17`

As we are talking about inches, we must take the positive one.

So:

• `"Length" = x = 20 " inches"`
• `"Width" = y = x-3 = 17 " inches"`