A rectangular prism has the following characteristics. It has a volume of 71 cubic inches. The sum of the three lengths is 14. The width is 2 less than the length. The length is 5 more than the height. What are the dimensions of this rectangular prism? Need help on finding this information.
Use process similar to previous post.
To find the dimensions of the rectangular prism, we can use the given information and create a system of equations:
Let's denote the length of the prism as L, the width as W, and the height as H.
From the given information:
1) The volume of the prism is 71 cubic inches:
The volume of a rectangular prism is given by the formula V = L x W x H. Substituting the values, we have 71 = L x W x H.
2) The sum of the three lengths is 14: L + W + H = 14.
3) The width is 2 less than the length: W = L - 2.
4) The length is 5 more than the height: L = H + 5.
Now, we can solve this system of equations to find the values of L, W, and H.
Substituting (3) and (4) into (2), we have:
(H + 5) + (H - 2) + H = 14.
Combining like terms, we get:
3H + 3 = 14.
Subtracting 3 from both sides, we have:
3H = 11.
Dividing both sides by 3, we get:
H = 11/3.
Plugging this value back into equation (4), we can find L:
L = (11/3) + 5 = 26/3.
Finally, substituting the values of L and W into equation (1), we can find W:
71 = (26/3) x (26/3 - 2) x (11/3).
Now, you can simplify the equation and solve for W.