Triangle $D E F$ is similar to triangle $A B C$.
Solve for $y$.
$$
y=
$$

Question

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Given that triangles $DEF$ and $ABC$ are similar, we can set up a proportion using corresponding sides. ‖ ‖ step 2 ⋮ The proportion based on the similarity is $\frac{DE}{BC} = \frac{DF}{BA}$. Substituting the given lengths, we get $\frac{37.5}{16.5} = \frac{20}{y}$. ‖ ‖ step 3 ⋮ To solve for $y$, cross-multiply to get $37.5y = 16.5 imes 20$. ‖ ‖ step 4 ⋮ Simplify the equation to find $y$ by dividing both sides by 37.5, resulting in $y = \frac{16.5 imes 20}{37.5}$. ‖ ‖ step 5 ⋮ Calculate the value of $y$ to get $y = \frac{330}{37.5}$. ‖ ‖ step 6 ⋮ Simplify the fraction to get $y = \frac{44}{5}$ or $y = 8.8$. ‖ ∻Answer∻ ⚹ $y = \frac{44}{5}$ or $y = 8.8$ ⚹ ∻Key Concept∻ ⚹Similar Triangles and Proportions⚹ ∻Explanation∻ ⚹When two triangles are similar, the ratios of the lengths of their corresponding sides are equal. This property is used to solve for unknown sides.⚹◊What is the formula for determining the similarity of two triangles based on their corresponding angles and side lengths⍭ Generate me a similar question◊

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