Question

The length of a rectangle is 3 cm more than the width. The area is 70cm^2. How do you find the dimensions of the rectangle?

Answer 1

If we write `w` for the width in `"cm"`, then `w(w+3) = 70`.

Hence we find `w = 7` (discarding negative solution `w = -10`).

So width `= 7"cm"` and length `= 10"cm"`

Explanation:

Let `w` stand for the width in `"cm"`.

Then the length in `"cm"` is `w + 3` and the area in `"cm"^2` is `w(w+3)`

So:

`70 = w(w+3) = w^2+3w`

Subtract `70` from both ends to get:

`w^2+3w-70 = 0`

There are a variety of ways to solve this, including the quadratic formula, but we can instead recognise that we're looking for a pair of factors of `70` which differ by `3`.

It should not take long to find `70 = 7 xx 10` fits the bill, hence we find:

`w^2+3w-70 = (w-7)(w+10)`

So `w^2+3w-70 = 0` has two solutions, viz `w = 7` and `w = -10`.

Since we're talking about lengths, we can ignore the negative solution leaving `w = 7`. That is the width is `7"cm"` and the length is `10"cm"`.