Question

Select the correct answer. A pizza parlor uses square prisms for their pizza boxes. Due to the crust rising, the height of their boxes is always 2 inches. Additionally, the volume of the pizza box must be 450 cubic inches to fit their standard-sized pizza. A worker determined that the equation 2x2 = 450 could be used to find the side length, x, of the box needed to reach that volume. Determine which statement is true about the solutions to the equation. A. The solutions are -30 and 30 and both are reasonable side lengths. B. The solutions are -15 and 15 and both are reasonable side lengths. C. The solutions are -15 and 15, but only 15 is a reasonable side length. D. The solutions are -30 and 30 but only 30 is a reasonable side length.

Answer 1

We are to find the side length of the box

Volume = Length * Breadth * Height

Volume of box = 450 cubic inches

Height of box = 2 inches

Length of box = x

Since it is a square prism, Breadth = Length = x

Therefore,

Volume = Length * Breadth * Height

⇒ 450 = 2 * x * x

⇒ 450 = 2x²

⇒ 2x² = 450

Divide the equation by 2

2x²/2 = 450/2

x² = 225

⇒√x² = √225

x = 15

The side length of the box is 15 inches

Answer 2

C. The solutions are -15 and 15, but only 15 is a reasonable side length.

Explanation:

The given equation is:

`2x^(2) =450`

We need to solve this quadratic equation to find the correct answer.

`2x^(2) =450\\x^(2)=(450)/(2)\\x^(2)=225\\x=√(225)=\±15`

As you can see, solutions are 15 and -15. However, when we talk about length, we always use positive numbers, because we cannot measure -15 inches.

Therefore, the correct answer is option C.