Create a polynomial using the given dimensions. Then, solve for height.
12 ft long by 4 ft high by 2 ft wide
Practice makes perfect
We can begin by creating a polynomial for the volume of the prism in terms of h, as the product of the given dimensions.
h ( h+8)(h-2)
Next, we simplify the expression.
We can split the equation into two parts and factor out the common factors.
( h^3+6h^2)+(-16h- 96)
⇕
h^2(h+6)-16(h+6)
⇕
(h^2-16)(h+6)
Notice that (h^2-16) is a difference of squares. This means that we can factor it as follows.
(h^2-16)(h+6)
⇕
(h+4)(h-4)(h+6)
Then, we can set each factor equal to 0 and solve for h.
rcl
h+4=0 & ⇒ & h= -4
h-4=0 & ⇒ & h=4
h+6=0 & ⇒ & h=-6
We can identify that the only positive solution is h=4. Therefore, the height is 4ft and we can use the given expressions for length and depth to find the other dimensions.
