Question

Math

Posted 2 months ago

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

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Answer from Sia

Posted 2 months ago

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 $37.5y = 16.5 \times 20$

step 4

Simplify the equation to find $y$ by dividing both sides by 37.5, resulting in $y = \frac{16.5 \times 20}{37.5}$

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.

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