Questions: If the two triangles are similar. What is the length of x to one decimal place?

If the two triangles are similar. What is the length of x to one decimal place?
Transcript text: If the two triangles are similar. What is the length of $x$ to one decimal place?
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Solution

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Solution Steps

Step 1: Identify the relationship between the triangles

Since the two triangles are similar, their corresponding sides are proportional.

Step 2: Set up the proportion

The sides of the triangles are given as:

  • Smaller triangle: \( x \) cm and 7 cm
  • Larger triangle: 17.6 cm and 19.6 cm

Set up the proportion: \[ \frac{x}{17.6} = \frac{7}{19.6} \]

Step 3: Solve for \( x \)

Cross-multiply to solve for \( x \): \[ x \cdot 19.6 = 7 \cdot 17.6 \] \[ x \cdot 19.6 = 123.2 \] \[ x = \frac{123.2}{19.6} \] \[ x \approx 6.3 \]

Final Answer

The length of \( x \) is approximately 6.3 cm.

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