Question

Gabriel is designing equally sized horse stalls that are each in the shape of a rectangular prism. Each stall must be 9 feet high and have a volume of 1,080 cubic feet. The length of each stall should be 2 feet longer than its width.
The volume of a rectangular prism is found using the formula V = l · w · h, where l is the length, w is the width, and h is the height.

Complete the equation that represents the volume of a stall in terms of its width of x feet.

Answer 1

Answer:

The equation is $9x(x+2)=1,080.$

The solution of the equation is x=10.

Step-by-step explanation:

The volume of a rectangular prism is found using the formula V = l · w · h, where l is the length, w is the width, and h is the height.

Let x ft be the widht of the stall, then the length of the stall is x+2 ft. If each stall must be 9 ft high, then the volume of the stall is $V=x\cdot (x+2)\cdot 9=9x(x+2)\ ft^3.$

The volume of each stall is $1,080\ ft^3,$ then

$9x(x+2)=1,080,\\ \\x(x+2)=120,\\ \\x^2+2x-120=0,\\ \\D=2^2-4\cdot (-120)=4+480=484=22^2,\\ \\x_{1,2}=\dfrac{-2\pm 22}{2}=-12,\ 10.$

The width cannot be negative, thus, $x=10.$