Question

The length of a rectangle is 4 inches more than its width, and its perimeter is 34 inches. What is the length and width of the rectangle?

Answer 1

Length `l = 10.5”`, Width `w = 6.5”`

Explanation:

Perimeter `P= 2l + 2w`

Given `l =( w + 4)”, P = 34”`

`:. 34 = 2(w+4) + 2w`

`4w + 8 = 34`

`w = 26/4 = 6.5”`

`l = w + 4 = 6.5 + 4 = 10.5”`

Answer 2

length is `10.5` inches

width is `6.5` inches

Explanation:

Let length be `l`
Let width be `w`
Let perimeter be `P`

First, we must construct an equation for these variables:

`l=w+4`

`P=34`

But, Perimeter of a rectangle `=l+w+l+w`

`=2l+2w`

So:

`34=2l+2w`

But, since `l=w+4`, we can substitute for `l`, having only the `w` variable:

`34=2(w+4)+2w`

`34=2w+8+2w`

`34=4w+8`

Solve for `w`:

`4w=34-8`

`4w=26`

`w=26/4`

`w=6.5` inches

Now, we can substitute `6.5` for `w` in the Perimeter Equation:

`34=2l+2w`

becomes:

`34=2l+2*6.5`

`34=2l+13`

Solve for `l`:

`2l=34-13`

`2l=21`

`l=21/2`

`l=10.5` inches

Thus, length is `10.5` inches

Thus, width is `6.5` inches