The surface area of a rectangular prism is A=2lw+2lh+2wh, where l, w, and h are the length, width, and height of the prism, respectively. Determine the width of a rectangular prism with a surface area of 930
square units if its length is 12
units and its height is 9
units.(1 point)
Responses
17
units
17 units
121112 units
12 and StartFraction 11 over 12 EndFraction units
81118 units
8 and Start Fraction 11 over 18 End Fraction units
108
units
To find the width of the rectangular prism, we need to plug in the given values into the equation for the surface area and solve for the width.
From the equation for the surface area:
A = 2lw + 2lh + 2wh
Substitute the given values:
930 = 2(12)(w) + 2(12)(9) + 2(w)(9)
Simplify:
930 = 24w + 216 + 18w
Combine like terms:
930 = 42w + 216
Subtract 216 from both sides:
930 - 216 = 42w
714 = 42w
Divide both sides by 42:
714/42 = w
17 = w
The width of the rectangular prism is 17 units.