Question

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list the side lengths of △cde in order from shortest to longest.
c
68y
e
47y
65y
d
□ < □ < □
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Explanation:

Step1: Recall Triangle Angle-Side Relationship

In a triangle, the larger the angle, the longer the side opposite to it. So we first identify the angles of $\triangle CDE$: $\angle C = 68y$, $\angle D = 65y$, $\angle E = 47y$.

Step2: Order the Angles from Smallest to Largest

Compare the angle measures: $47y < 65y < 68y$. So $\angle E < \angle D < \angle C$.

Step3: Identify the Opposite Sides

• Side opposite $\angle E$ is $CD$.
• Side opposite $\angle D$ is $CE$.
• Side opposite $\angle C$ is $DE$.

Step4: Order the Sides by Opposite Angles

Since $\angle E < \angle D < \angle C$, their opposite sides follow the same order: $CD < CE < DE$.

Answer:

$CD < CE < DE$