Question

find the missing side length in these similar solids.
image of two similar rectangular prisms: left one has length 12 cm, height 8 cm; right one has height 6 cm, missing length? cm

Explanation:

Step1: Set up similarity proportion

Since the solids are similar, their corresponding sides are proportional. Let the missing side be $x$.
$$\frac{12}{x} = \frac{8}{6}$$

Step2: Cross-multiply to solve for $x$

Cross-multiply to isolate $x$.
$$8x = 12 \times 6$$
$$8x = 72$$

Step3: Divide to find $x$

Divide both sides by 8 to get the value of $x$.
$$x = \frac{72}{8}$$

Answer:

9 cm