Question

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

Explanation:

Step1: Sum angles to 180°

$$(b+57) + (b+66) + 7b = 180$$

Step2: Simplify to solve for b

$$9b + 123 = 180$$
$$9b = 57$$
$$b = \frac{57}{9} = \frac{19}{3} \approx 6.33$$

Step3: Calculate each angle

• $\angle E = b+57 = \frac{19}{3} + 57 = \frac{19+171}{3} = \frac{190}{3} \approx 63.33^\circ$
• $\angle C = b+66 = \frac{19}{3} + 66 = \frac{19+198}{3} = \frac{217}{3} \approx 72.33^\circ$
• $\angle D = 7b = 7\times\frac{19}{3} = \frac{133}{3} \approx 44.33^\circ$

Step4: Match sides to opposite angles

Side opposite $\angle D$ (smallest angle): $EC$
Side opposite $\angle E$ (middle angle): $CD$
Side opposite $\angle C$ (largest angle): $ED$

Answer:

$EC < CD < ED$