Question

triangle def is similar to triangle ghi. find the measure of side ig. figures are not drawn to scale.

Explanation:

Step1: Set up proportion

Since the triangles are similar, the ratios of corresponding sides are equal. Let $IG = x$. The ratio of the hypotenuse to the vertical - side in $\triangle DEF$ is the same as the ratio in $\triangle GHI$. So, $\frac{DF}{EF}=\frac{IG}{HI}$. We know that $DF = 4$, $EF = 2$, and $HI=12.1$. The proportion is $\frac{4}{2}=\frac{x}{12.1}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{4}{2}=\frac{x}{12.1}$ gives us $2x=4\times12.1$.

Step3: Solve for x

First, calculate $4\times12.1 = 48.4$. Then, solve the equation $2x = 48.4$ for $x$ by dividing both sides by 2. So, $x=\frac{48.4}{2}=24.2$.

Answer:

$24.2$