One good way to start word problems is by listing the information provided, then converting it to math terms.
Height is 2 inches shorter than the length.
Width is 2 inches shorter than the length.
Volume of the prism is 40 cubic inches.
Our next job is to translate the given information in math terms. Let's start with the volume of a rectangular prism.
V=Length * Width * HeightIn this formula, volume is related to the height and width. We will assign variables to each component.
Length&=l
Width&=l-2
Height&=l-2
Now we can simplify the formula and solve for the length and use that to get the width and the height.
Now we need to solve for l. Since this is a cubic equation, we can graph graph it. There are a couple of options for graphing. One way is to rearrange the equation so it is equal to 0 and then rewrite it as a function.
l^3-4l^2+4l=40
⇕
l^3-4l^2+4l-40=0
⇕
f(x)=x^3-4x^2+4x-40
Let's look at the graph and find the zeros.
We can see that f(x) has a zero at x = 4.87. Let's go back to our definition of variables to find the dimensions of the rectangular prism. Remember, in this case, x represents the length.
Length:& l &=4.87
Width:& l-2 &=2.87
Height:& l-2 &=2.87
