The length of a rectangle is nine more than twice the width. Write a simplified expression that could be used to find the perimeter of the rectangle.

Answer 1

First thing I would ask you to do, if it helps you to visualize, is to draw a rectangle and label 1 of the 2 shorter sides as the width (w) and 1 of the 2 longer sides as the length (l).

The formula for the perimeter of a rectangle is 2w + 2l.

For this particular math question, they tell us that the length (l) of the rectangle is actually the same as or EQUAL TO 'nine more than twice the width (w)'.

So, l = 2w + 9

and w = w

Then, we can write the expression representing the perimeter of this rectangle as follows:

2w + 2l - then we will substitute (2w + 9) for l (seen in the explanation above)

2w + 2(2w + 9) - then, apply the distributive property

2w + 4w + 18 - and, finally, combine like terms

6w + 18

Answer 2

Let w=width and l=length. Then l=2w+9 (twice the width and then 9 more than that).

Perimeter is the outside edge of the rectangle, which has 4 sides. 2 of those are the length and the other 2 are the width. So if we let p=perimeter, then p=2l+2w.

Now we substitute 2w+9 in for l, since we found that l=2w+9. So now we have p=2(2w+9)+2w.

Distributing the 2 gives us p=4w+18+2w.

Combining the w's gives us p=6w+18.