Question

list the side lengths of δstu in order from shortest to longest.

Explanation:

Step1: Sum triangle angles to 180°

$$13w + 24w + (w+66) = 180$$

Step2: Simplify and solve for $w$

$$38w + 66 = 180 \\ 38w = 114 \\ w = 3$$

Step3: Calculate each angle

• $\angle S = 13(3) = 39^\circ$
• $\angle T = 24(3) = 72^\circ$
• $\angle U = 3+66 = 69^\circ$

Step4: Match angles to opposite sides

Shortest side is opposite smallest angle ($\angle S$: side $TU$), middle side opposite middle angle ($\angle U$: side $ST$), longest side opposite largest angle ($\angle T$: side $SU$).

Answer:

$TU < SU < ST$