The length of a rectangular prism is four times the width. The height of the prism is 8 ft. If the volume of the prism is 160 ft^3, what is the width of the prism? Round to the nearest tenth of a foot.

Please solve and explain. Thanks

let the width be x

then length = 4x
height = 8

volume = w x l x h
160 = x(3x)(8)
24x^2 = 160
x^2 = 5x = √5 = 2.236.. or appr 2.2

yall the answer is right it is 2.2 ft if you're looking for the Savvas realize answer

2.2

To solve this problem, we can use the formula for the volume of a rectangular prism:

Volume = Length * Width * Height

Given that the height is 8 ft and the volume is 160 ft³, we can substitute these values into the formula:

160 ft³ = Length * Width * 8 ft

Now we need to find the relationship between the length and the width. The problem states that the length is four times the width. We can represent this relationship as:

Length = 4 * Width

Substituting this into the equation, we get:

160 ft³ = (4 * Width) * Width * 8 ft

Simplifying the equation gives us:

160 ft³ = 32 * Width²

Now we can solve for the width by isolating it on one side of the equation. Dividing both sides by 32 gives us:

5 ft² = Width²

Taking the square root of both sides, we find:

Width = √(5 ft²)

Using a calculator, we can approximate the square root to the nearest tenth of a foot. The width is approximately 2.236 ft (rounded to the nearest tenth).

Therefore, the width of the rectangular prism is approximately 2.2 ft.