A right rectangular prism has an area of 20 square units and a height of 3 units. What is the volume?
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The area of a right rectangular prism is given by the formula:
Area = 2lw + 2lh + 2wh
We are given that the area is 20 square units and the height is 3 units. If we substitute these values into the formula, we have:
20 = 2lw + 2l(3) + 2w(3)
Simplifying this equation, we get:
20 = 2lw + 6l + 6w
Next, we can factor out a 2 from the first two terms:
20 = 2(lw + 3l) + 6w
Then, we can subtract 6w from both sides of the equation:
20 - 6w = 2(lw + 3l)
Dividing both sides by 2 gives:
10 - 3w = lw + 3l
Next, we can factor out an l from the terms on the right-hand side:
10 - 3w = l(w + 3)
Since the left-hand side is a constant, the right-hand side must also be a constant. Therefore, we have:
w + 3 = 0
Solving for w gives:
w = -3
Since the width cannot be negative, we can conclude that the width must be 3 units.
Now, we can substitute the values of l = 20 and w = 3 into the formula for volume of a right rectangular prism:
Volume = lwh
Volume = 20(3)(3) = 180 cubic units
Therefore, the volume of the right rectangular prism is 180 cubic units.