# The area of a rectangle is 300 cm squared. what is the length and width if the ratio of length to width is 4:3?

L = 20 and W = 15

#### Explanation:

Let's review what is known about the rectangle in question - the area is 300 cm squared and the ratio of the Length to the Width (which I'll shorten to L and W) is 4:3.

Let's start with the ratio. We know that they are related to each other - 4 of a basic unit of length for L and 3 of that same basic unit of length for W. So we can say that

L = $4 x$ and W = $3 x$

We also know from the formula for the area of a rectangle that LW = Area of the rectangle. Substituting in the terms with the x's in them gives us

$\left(4 x\right) \left(3 x\right) = 300$

so let's solve for x:

$12 {x}^{2} = 300$

${x}^{2} = \frac{300}{12} = 25$

$x = \sqrt{25} = 5$ (ignoring the negative root since that makes no sense in this application)

Substituting x back into our equations for L and W, we get

L = $4 \left(5\right) = 20$ and W = $3 \left(5\right) = 15$

Checking our work - there is a ratio of L:W of 4:3. And LW = $20 \cdot 15 = 300$