Question

find the length of \\(\overline{sv}\\).
options: a 8, b 17, c 18, d 13

Explanation:

Step1: Use the triangle - proportionality theorem

If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally. Here, \(\angle S=\angle S\) (common angle) and \(\angle SWV=\angle T\) (corresponding angles as \(WV\parallel TU\)), so \(\triangle SWV\sim\triangle STU\). Then \(\frac{SW}{ST}=\frac{SV}{SU}\). Let \(SV = x\), \(ST=42\), \(SW = 28\), \(SU=x + 26\).

Step2: Set up the proportion equation

\(\frac{28}{42}=\frac{x}{x + 26}\). Cross - multiply: \(28(x + 26)=42x\).

Step3: Expand and solve the equation

Expand \(28(x + 26)\): \(28x+728 = 42x\). Subtract \(28x\) from both sides: \(728=42x - 28x\), so \(14x = 728\). Divide both sides by \(14\): \(x=\frac{728}{14}=13\).

Answer:

D. 13