Question

Order the sides of the triangle from shortest to longest.

Answer 1

Answers:

• Shortest Length = LN
• Middle Length = LM
• Longest Length = MN

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Explanation:

Let's find the missing angle.

For any triangle, the three interior angles always add to 180

L+M+N = 180

75+50+N = 180

N+125 = 180

N = 180-125

N = 55

So we know the three angles of the triangle are

• L = 75
• M = 50
• N = 55

We see that M = 50 is the smallest angle, so the smallest side is the segment opposite this angle. The smallest side is LN. The smallest side is always opposite the smallest angle.

Similarly, the largest side is always opposite the largest angle. The largest angle here is L = 75, so the largest side is MN.

The middle side must therefore be LM.

The diagram below shows a visual summary.