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?

1 Answer

L = 20 and W = 15


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 = #4x# and W = #3x#

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

#(4x)(3x) = 300#

so let's solve for x:

#12x^2 = 300#

#x^2 = 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(5)=20# and W = #3(5)=15#

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