Question

list the side lengths of \\( \delta r s t \\) in order from shortest to

Explanation:

Step1: Find the value of \(w\)

The sum of angles in a triangle is \(180^{\circ}\). So, \((w + 18)+(w - 11)+(w + 8)=180\).
Combine like terms: \(3w+15 = 180\).
Subtract \(15\) from both sides: \(3w=165\).
Divide by \(3\): \(w = 55\).

Step2: Calculate each angle

• \(\angle S=w + 18=55+18 = 73^{\circ}\)
• \(\angle R=w - 11=55-11 = 44^{\circ}\)
• \(\angle T=w + 8=55+8 = 63^{\circ}\)

Step3: Relate angles to opposite sides

In a triangle, the side opposite the smaller angle is shorter.
\(\angle R(44^{\circ})<\angle T(63^{\circ})<\angle S(73^{\circ})\)
The side opposite \(\angle R\) is \(ST\), opposite \(\angle T\) is \(SR\), and opposite \(\angle S\) is \(RT\).

Answer:

\(ST