Question

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

Explanation:

Step1: Find the scale - factor

Since the two quadrilaterals are scaled copies, we can find the scale - factor by comparing corresponding sides. Let's use the sides of length 40 and 32. The scale - factor $k$ is given by the ratio of the corresponding sides of the scaled copy (quadrilateral $H$) to the original (quadrilateral $G$). So, $k=\frac{32}{40}=\frac{4}{5}$.

Step2: Calculate the value of $i$

We know that the side of length 45 in quadrilateral $G$ corresponds to side $i$ in quadrilateral $H$. Using the scale - factor, we have $i = 45\times k$. Substituting $k=\frac{4}{5}$ into the equation, we get $i = 45\times\frac{4}{5}=36$.

Answer:

36