Questions: The rectangular prisms shown below are similar. What are the values of x and y? x : y :

Solution Steps

Since the two rectangular prisms are similar, their corresponding sides are proportional. We can set up the following proportions:

• $\frac{x}{3} = \frac{9}{12}$
• $\frac{y}{8} = \frac{9}{12}$

To solve for $x$, we can cross-multiply the first proportion:

$12x = 3 \cdot 9$ $12x = 27$ $x = \frac{27}{12}$ $x = \frac{9}{4}$ $x = 2.25$

To solve for $y$, we can cross-multiply the second proportion:

$12y = 8 \cdot 9$ $12y = 72$ $y = \frac{72}{12}$ $y = 6$

Final Answer