rectangular prism with a volume of 72 cubic inches; sum of the 3 lengths is 13; width is half of the height; the length is one more than the width what are the dimensions of the rectangular prism
To find the dimensions of a rectangular prism, we can use the given information and set up a system of equations.
Let's assume the length of the rectangular prism is L, the width is W, and the height is H.
Given:
1) The volume of the rectangular prism is 72 cubic inches:
Volume = Length × Width × Height
72 = L × W × H
2) The sum of the 3 lengths is 13:
L + W + H = 13
3) The width is half of the height:
W = 0.5H
4) The length is one more than the width:
L = W + 1
Now we can solve the system of equations:
Substitute equation 3) into equation 4) to express L in terms of H:
L = 0.5H + 1
Substitute L and W from equations 3) and 4) into equation 2):
(0.5H + 1) + 0.5H + H = 13
Combine like terms:
2H + 1 = 13
Subtract 1 from both sides:
2H = 12
Divide both sides by 2:
H = 6
Substitute H = 6 into equation 3) to find W:
W = 0.5(6)
W = 3
Substitute H = 6 and W = 3 into equation 4) to find L:
L = 3 + 1
L = 4
Therefore, the dimensions of the rectangular prism are:
Length (L) = 4 inches
Width (W) = 3 inches
Height (H) = 6 inches
Which rectangular prisms have a volume of 72 cubic units?
A rectangular prism has a volume of 72 cubic units. How many unit cubes will fill the rectangular prism
i do not know what the answer is to the qustion
w+1 + 2w + w = 13
4w+1 = 13
w = 3
check:
3+4+6 = 13
3*4*6 = 72