Question

1. solve for x.

12 + 115x
1250
360
540

Explanation:

1. Assume the triangles are similar (since no other information about the relationship between the two triangles is given, a common - approach in such geometry problems is to assume similarity if side - length ratios are involved):

• If two triangles are similar, the ratios of their corresponding sides are equal. Let's assume that the sides of the two triangles are in proportion. Suppose that the side \(12 + 115x\) in \(\triangle SQR\) corresponds to the side \(360\) in \(\triangle UVW\), and the side \(1250\) in \(\triangle SQR\) corresponds to the side \(540\) in \(\triangle UVW\). Then we can set up the proportion:
• \(\frac{12 + 115x}{360}=\frac{1250}{540}\)

1. Cross - multiply the proportion:

• Cross - multiplying gives us \(540\times(12 + 115x)=360\times1250\).
• First, expand the left - hand side: \(540\times12+540\times115x = 360\times1250\).
• Calculate \(540\times12 = 6480\) and \(360\times1250=450000\). So the equation becomes \(6480 + 62100x=450000\).

1. Isolate the variable term:

• Subtract \(6480\) from both sides of the equation: \(62100x=450000 - 6480\).
• \(450000−6480 = 443520\). So, \(62100x = 443520\).

1. Solve for \(x\):

• Divide both sides of the equation by \(62100\): \(x=\frac{443520}{62100}\).
• Simplify the fraction \(\frac{443520}{62100}=\frac{443520\div180}{62100\div180}=\frac{2464}{345}\approx7.14\).

Step1: Set up proportion

Assume similar triangles, \(\frac{12 + 115x}{360}=\frac{1250}{540}\)

Step2: Cross - multiply

\(540\times(12 + 115x)=360\times1250\), which expands to \(6480 + 62100x=450000\)

Step3: Isolate variable term

\(62100x=450000 - 6480=443520\)

Step4: Solve for \(x\)

\(x = \frac{443520}{62100}=\frac{2464}{345}\)

Answer:

\(x=\frac{2464}{345}\)