Question

quadrilateral i is a scaled copy of quadrilateral h. what is the value of g?

Explanation:

Step1: Find the scale - factor

Since the two quadrilaterals are scaled copies, the ratios of corresponding sides are equal. Let's find the scale - factor by comparing the known corresponding sides. The ratio of the vertical sides of the two quadrilaterals gives the scale - factor. The vertical side of quadrilateral $H$ is $1\frac{1}{4}=\frac{5}{4}$, and the vertical side of quadrilateral $I$ is $1$. The scale - factor $k$ from $H$ to $I$ is $\frac{1}{\frac{5}{4}}=\frac{4}{5}$.

Step2: Calculate the value of $g$

We know that the horizontal side of quadrilateral $H$ is $\frac{5}{8}$. To find the corresponding side $g$ in quadrilateral $I$, we multiply the length of the corresponding side in $H$ by the scale - factor. So $g=\frac{5}{8}\times\frac{4}{5}$.
$g = \frac{5\times4}{8\times5}=\frac{20}{40}=\frac{1}{2}$

Answer:

$\frac{1}{2}$