Question

introduction to similarity (tues 1/20)
find the missing side length.
12
?
24
25
15

Explanation:

Step1: Identify the scale factor

Since the trapezoids are similar, the ratios of corresponding sides are equal. First, find the scale factor using the top bases: $\frac{15}{12}=\frac{5}{4}$ or using the bottom bases: $\frac{24}{x}$ (wait, no, the bottom base of the second trapezoid? Wait, no, the first trapezoid has bottom base 24, top base 12; the second has top base 15, side 25, and we need to find the side of the first. Wait, let's denote the first trapezoid's side as $x$, second as 25. The ratio of top bases: $12$ (first) to $15$ (second) is $\frac{12}{15}=\frac{4}{5}$. So the ratio of corresponding sides should be the same. So $\frac{x}{25}=\frac{4}{5}$? Wait, no, maybe the first trapezoid's top is 12, bottom 24; second's top is 15, bottom let's see, but the side of the second is 25. Wait, maybe the ratio of top to top is $12/15 = 4/5$, so the ratio of side to side should be the same. So let the missing side be $x$. Then $\frac{x}{25}=\frac{12}{15}$. Simplify $\frac{12}{15}=\frac{4}{5}$. So $x = 25\times\frac{4}{5}$.

Step2: Calculate the missing side

$25\times\frac{4}{5} = 5\times4 = 20$? Wait, no, wait: $\frac{x}{25}=\frac{12}{15}$ → cross-multiply: $15x = 25\times12$ → $15x = 300$ → $x = 300/15 = 20$. Wait, but let's check with the bottom bases. First bottom is 24, second bottom: let's see, ratio of top is 12/15=4/5, so bottom of second should be 24/(4/5)=24*(5/4)=30. Then the side of second is 25, so side of first is x, so x/25=12/15 → x=20. Yes, that works.

Answer:

20