Question

list the side lengths of $\triangle rst$ in order from shortest to longest.
$\square < \square < \square$
submit

Explanation:

Step1: Sum angles to 180°

$$(10y-15)+(34y-96)+(y+66)=180$$

Step2: Simplify left side

$$45y - 45 = 180$$

Step3: Solve for y

$$45y=225 \implies y=5$$

Step4: Calculate each angle

• $\angle T = 10(5)-15=35^\circ$
• $\angle R = 34(5)-96=74^\circ$
• $\angle S = 5+66=71^\circ$

Step5: Match sides to opposite angles

Side opposite $\angle T$: $RS$
Side opposite $\angle S$: $RT$
Side opposite $\angle R$: $ST$
Order angles: $35^\circ < 71^\circ < 74^\circ$

Answer:

$RS < ST < RT$