A rectangular prism has length x+2, width x+1, height 4, and volume 24. find the length and the width?
4(x+1)(x+2) = 24
(x+1)(x+2) = 6
I think you know two consecutive integers whose product is 6.
To find the length and width of the rectangular prism, you need to solve for the value of x in the given equation.
The formula for the volume of a rectangular prism is given by:
Volume = length × width × height
In this case, the volume of the rectangular prism is given as 24 and the height is 4. The length is x + 2, and the width is x + 1. So we can set up the equation:
24 = (x + 2) × (x + 1) × 4
To solve this equation, first multiply (x + 2) and (x + 1):
24 = (4x + 4) × 4
Next, simplify the equation further:
24 = 16x + 16
Now, to isolate the variable x, we need to subtract 16 from both sides:
24 - 16 = 16x
8 = 16x
Dividing both sides by 16, we get:
8/16 = x
Simplifying further:
1/2 = x
Therefore, the value of x is 1/2.
Now, you can substitute this value back into the expressions for the length and width of the rectangular prism to find their values:
Length = x + 2
Length = (1/2) + 2 = 2.5
Width = x + 1
Width = (1/2) + 1 = 1.5
Thus, the length of the rectangular prism is 2.5 and the width is 1.5.