Question

rt is a midsegment of \\( \triangle suv \\).
if \\( uv = x \\) and \\( rt = x - 15 \\), what is \\( uv \\)?

Explanation:

Step1: Apply the midsegment theorem

The midsegment theorem states that the length of a midsegment of a triangle is half the length of the parallel side. So, \( RT=\frac{1}{2}UV \).

Step2: Substitute the given expressions

Given \( UV = x \) and \( RT=x - 15 \), substitute into the equation \( RT=\frac{1}{2}UV \). We get \( x-15=\frac{1}{2}x \).

Step3: Solve the equation for \( x \)

Subtract \( \frac{1}{2}x \) from both sides: \( x-\frac{1}{2}x-15 = 0 \), which simplifies to \( \frac{1}{2}x-15=0 \). Then add 15 to both sides: \( \frac{1}{2}x=15 \). Multiply both sides by 2: \( x = 30 \).

Answer:

\( 30 \)