Rewrite the dimensions in terms of the width. Then, solve for width.
6 ft wide by 2 feet long by 15 ft high
Practice makes perfect
Let's begin by writing the other dimensions in terms of the width, w.
height= w+9
length=w-4
We can create a polynomial for the volume of the prism in terms of w, as the product of these dimensions.
w ( w+9)(w-4)Next, we simplify the expression.
We can split the equation into two parts and factor out the common factors.
( w^3+5w^2)+(-36w- 180)
⇕
w^2(w+5)-36(w+5)
⇕
(w^2-36)(w+5)
Notice that (w^2-36) is a difference of squares meaning it can be factored as follows.
(w^2-36)(w+5)
⇕
(w+6)(w-6)(w+5)
Then, we can set each factor equal to 0 and solve for w.
rcl
w+6=0 & ⇒ & w= -6
w-6=0 & ⇒ & w=6
w+5=0 & ⇒ & w=-5
We can identify that the only positive solution is w=6. Therefore, the width is 6ft and we can use initial expressions we created for length and height to find the other dimensions.
