# Find the dimensions of a rectangle

by a visitor

##### Question
The area of a rectangle is 45 square cm. If the length is 4 cm greater than the width, what is the dimensions of the rectangle?

The picture below shows the rectangle with the area of 45cm2. Now, let the width be w. Since, the length is 4cm greater than the width, the length will be w+4 cm.

Before we can find the dimensions of the rectangle, we need find w first. Here's how:

1) Write an equation that relates 45cm2, w+4 and w.
To do so, we know that the area of the rectangle, 45cm2 can be found by multiplying w with  w+4. Hence, we have:

To continue, we need to remove the bracket and simplify the equation. This is shown below:

Notice that, now we have a quadratic equation:

To find w, we need to solve the quadratic equation. One way to do so is to factorize the quadratic equation. Hence, we have:

Now, since w is the width of a rectangle. There is no way it can be a negative number. Therefore, w must be 5.
With w = 5. The...

...and the...
Below is the rectangle with its dimensions:

### Comments for Find the dimensions of a rectangle

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 Jun 01, 2015 Rating Reply to comment from May 31, 2015 by: Visual Math The perimeter of a rectangle is its two times its length and width combined, expressed in this way: P = 2 x (l + w) Now then, given that the length is three cm more than twice the width, we can express the length in terms of the width in this way: l = 2w + 3 Thus, if we replace all the variables with the information we have, we can find out its dimensions: P = 2 x (l + w) 84 = 2 x ((2w + 3) + w) 84 = 2 x (3w + 3) 84 = 6w + 6 6w = 84 - 6 6w = 78 w = 78/6 w = 13cm Given that w is 13cm, we can then use it to find l: l = 2w + 3 l = 2(13) + 3 l = 26 + 3 l = 29cm

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