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The triangles pictured are similar. Fill in the blanks to solve for the missing side length.

(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Set up equivalent ratios: 4x=
Response area

Cross multiply: Response area =36
​​​​​​​

Solve for x: x=
Response area miles

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1 answer

To solve for the missing side length using the properties of similar triangles, you follow these steps:

  1. Set up equivalent ratios: Given that the triangles are similar, you can set up the ratio of the corresponding sides. For example, if you have a triangle with a side of length 4 and the corresponding side in the other triangle represented as \( x \), the equation could look like: \[ \frac{4}{x} = \frac{\text{other corresponding side length}}{\text{given side length}} \] In this case, it seems that \( 4x = \text{other corresponding side length} \).

  2. Cross multiply: After setting the equivalent ratios, you cross multiply. For example: \[ 4x = 36 \]

  3. Solve for x: To find \( x \), you can do the following: \[ x = \frac{36}{4} \]

So, to fill in your responses based on this procedure:

  • Fill in 4x = 36 for the equivalent ratios.
  • Solve for \( x \) and you would find that \( x = 9 \).

So, your answers would be:

  • Set up equivalent ratios: 4x = 36
  • Cross multiply: Response area = 36
  • Solve for x: x = 9 miles

If there’s any more specific information on which sides correspond or additional values, feel free to provide that for a more tailored answer!