Question

the two trapezoids shown below are similar.
what is the value of x?
x = \square

Explanation:

Step1: Recall similarity ratio

For similar figures, corresponding sides are proportional. Let's identify corresponding sides. The small trapezoid has a side of length $\frac{1}{4}$ and the large one has $1\frac{1}{4}=\frac{5}{4}$. The small trapezoid's base is $\frac{1}{2}$, and the large one's base is $x$. So the ratio of corresponding sides should be equal. So we set up the proportion: $\frac{\frac{1}{4}}{\frac{5}{4}}=\frac{\frac{1}{2}}{x}$.

Step2: Simplify the left ratio

Simplify $\frac{\frac{1}{4}}{\frac{5}{4}}$. Dividing fractions: $\frac{1}{4}\div\frac{5}{4}=\frac{1}{4}\times\frac{4}{5}=\frac{1}{5}$. So the proportion becomes $\frac{1}{5}=\frac{\frac{1}{2}}{x}$.

Step3: Solve for x

Cross - multiply: $1\times x = 5\times\frac{1}{2}$. So $x=\frac{5}{2}=2\frac{1}{2}$.

Answer:

$\frac{5}{2}$ (or $2\frac{1}{2}$)