Question

Math

Posted 5 months ago

```
Solve for $x$.
$x=$
```

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Answer from Sia

Posted 5 months ago

Solution by Steps

step 1

Identify the similar triangles and their corresponding sides

step 2

Set up the proportion based on the similarity of triangles ABC and ADE

step 3

The proportion is $\frac{x}{6} = \frac{8}{11}$, since AB corresponds to BC and BD corresponds to DE

step 4

Solve for $x$ by cross-multiplying: $x \cdot 11 = 6 \cdot 8$

step 5

Calculate the value of $x$: $x = \frac{6 \cdot 8}{11}$

step 6

Simplify the fraction to find $x$: $x = \frac{48}{11}$

Answer

$x = \frac{48}{11}$

Key Concept

Similar Triangles and Proportions

Explanation

The lengths of corresponding sides of similar triangles are proportional. By setting up a proportion based on the given side lengths, we can solve for the unknown side.

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