Question

list the side lengths of $\triangle stu$ in order from shortest to longest.

Explanation:

Step1: Sum angles to 180°

$$(w+62) + 71w + 46w = 180$$

Step2: Simplify the equation

$$118w + 62 = 180$$

Step3: Solve for w

$$118w = 180 - 62 = 118 \implies w=1$$

Step4: Calculate each angle

• $\angle T = 1+62 = 63^\circ$
• $\angle S = 71\times1 = 71^\circ$
• $\angle U = 46\times1 = 46^\circ$

Step5: Match sides to opposite angles

Side opposite $\angle U$: $ST$
Side opposite $\angle T$: $SU$
Side opposite $\angle S$: $TU$
Order angles: $46^\circ < 63^\circ < 71^\circ$, so sides follow the same order.

Answer:

$ST < SU < TU$