Question

pentagon t is a scaled copy of pentagon s. what is the value of u?

Explanation:

Step1: Convert mixed - numbers to improper fractions

$1\frac{4}{5}=\frac{1\times5 + 4}{5}=\frac{9}{5}$ and $2\frac{7}{10}=\frac{2\times10+7}{10}=\frac{27}{10}$

Step2: Find the scale factor

The scale factor $k$ from pentagon $S$ to pentagon $T$ is found by dividing the corresponding side lengths. Let's use the vertical sides. $k=\frac{\frac{27}{10}}{\frac{9}{5}}=\frac{27}{10}\div\frac{9}{5}=\frac{27}{10}\times\frac{5}{9}=\frac{3}{2}$

Step3: Calculate the value of $u$

The side length in pentagon $S$ corresponding to side $u$ in pentagon $T$ is $1\frac{1}{5}=\frac{6}{5}$. Then $u=\frac{6}{5}\times\frac{3}{2}=\frac{18}{10} = 1\frac{8}{10}=1\frac{4}{5}$

Answer:

$1\frac{4}{5}$