Question

If the width of rectangle is 5 cm more than one-half of its length the perimeter is 70 cm, what are the dimensions of the rectangle?

Answer 1

The length is 20 cm and the width is 15 cm

Explanation:

First, let's call the width of our rectangle `w` and the length `l`.

From the problem we know:

`w = 1/2l + 5`

We also know the formula for the perimeter of a rectangle is:

`p = 2*l + 2*w`

So we can substitute `70` for `p` which is given in the problem and we can also substitute `1/2l + 5` for `w` and then solve for `l`:

`70 = 2*l + 2*(1/2l + 5)`

`70 = 2l + 1l + 10`

`70 = 3l + 10`

`70 - 10 = 3l + 10 - 10`

`60 = 3l`

`60/3 = (3l)/3`

`20 = l`

Now we can substitute `20` for `l` in the formula for `w` to find the width:

`w = 1/2 20 + 5`

`w = 10 + 5`

`w = 15`