Question

trapezoid x is a scaled copy of trapezoid w. trapezoid w has side - lengths 14, 15, 7. trapezoid x has side - lengths 19\frac{1}{4}, 20\frac{5}{8}, 9\frac{5}{8}. what scale factor takes trapezoid w to trapezoid x?

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ from trapezoid $W$ to trapezoid $X$ can be found by taking the ratio of corresponding side - lengths. Let's use the non - parallel sides.

Step2: Convert mixed numbers to improper fractions

$20\frac{5}{8}=\frac{20\times8 + 5}{8}=\frac{160+5}{8}=\frac{165}{8}$ and $15=\frac{15}{1}$.

Step3: Calculate the scale factor

$k=\frac{20\frac{5}{8}}{15}=\frac{\frac{165}{8}}{15}=\frac{165}{8}\times\frac{1}{15}=\frac{165}{120}=\frac{11}{8}=1\frac{3}{8}$

Answer:

$1\frac{3}{8}$