What is the missing width of a rectangular prism with a length of 6 cm, a height of 4 cm, and a surface area of 188 cm^2 ?(1 point)
To find the missing width of the rectangular prism, we first need to find the area of the rectangular prism's two other faces - the front and back faces.
Given that the length is 6 cm and the height is 4 cm, this means that the front and back faces have an area of:
6 cm * 4 cm = 24 cm^2
Since the total surface area of the rectangular prism is 188 cm^2 and the area of the front and back faces is 24 cm^2, the area of the remaining four sides (2 sides) is:
188 cm^2 - 24 cm^2 = 164 cm^2
Since the surface area of a rectangular prism is given by the formula:
Surface Area = 2lw + 2lh + 2wh
And we already know the length (l) is 6 cm, height (h) is 4 cm, and the total surface area is 164 cm^2, we can substitute these values into the formula and find the missing width (w).
164 cm^2 = 2(6)w + 2(4)w + 2(6)(4)
164 cm^2 = 12w + 8w + 48
164 cm^2 = 20w + 48
116 cm^2 = 20w
w = 116 cm^2 / 20
w = 5.8 cm
Therefore, the missing width of the rectangular prism is 5.8 cm.