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

Question

(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: 39=
Response area

Cross multiply: 3x=
Response area

Solve for x: x=
Response area miles

Answer 1

To solve for the missing side length in similar triangles using proportions, we can follow these steps:

1. Set up equivalent ratios: Assuming we have one side length of the first triangle as 39, and let's say the corresponding side length of the second triangle is denoted by 'x'. Thus, we can set up the ratio as follows:

   \( \frac{39}{x} = \frac{3}{k} \)

   (Here, \( k \) is the known side length corresponding to '3'.)

   You should insert 39 = in the first response area.

2. Cross multiply: Now, cross-multiply to set the equation for solving \( x \):

   \( 39 \cdot k = 3 \cdot x \)

   So you would write in the response area: 3x =.

3. Solve for x: Rearranging gives us:

   \( x = \frac{39 \cdot k}{3} \)

   This would result in the final value for 'x', which can be simplified. If you know the value of 'k', you can plug it in here. For now, let's keep it as:

   x = (result after plugging in the values, for example if \( k = 13 \), then ( x = \frac{39 \cdot 13}{3} = 169)

   Enter the calculated value of x in the final response area.

To summarize, here are the responses:

• Set up equivalent ratios: 39=
• Cross multiply: 3x=
• Solve for x: x= (final value in miles)