Question

question
the bases of the prism below are rectangles. if the prisms height measures 5 units and its volume is 135 units³, solve for x.
answer
attempt 1 out of 2
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Explanation:

Step1: Recall the volume formula for a rectangular prism

The volume formula for a rectangular prism is \(V = l\times w\times h\). Here, the base has dimensions \(x\) and \(9\) (so the area of the base \(B=x\times9 = 9x\)), and the height \(h = 5\). The volume formula can also be written as \(V=B\times h\). Substituting the values we know, we get \(135=9x\times5\).

Step2: Simplify the right - hand side of the equation

First, simplify \(9x\times5\). Using the associative property of multiplication, \(9x\times5=(9\times5)x=45x\). So the equation becomes \(135 = 45x\).

Step3: Solve for \(x\)

To solve for \(x\), divide both sides of the equation \(135 = 45x\) by \(45\). We have \(x=\frac{135}{45}\).

Answer:

\(x = 3\)