5. In XYZ, 2X = 3Y = 6Z, find the longest and shortest sides
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• 2x = 6z
- Thus x = 3z
• 3y = 6z
- Thus y = 2z
- Now we know that in a triangle sum of all angles is 180
- So ,
• x + y + z = 180
• 3z + 2z + z = 180
• 6z = 180
• z = 30
- Now x would be 90 and y would be 60
- The longest side would be the side opposite to the largest angle so longest side must be YZ .
- Thus x = 3z
• 3y = 6z
- Thus y = 2z
- Now we know that in a triangle sum of all angles is 180
- So ,
• x + y + z = 180
• 3z + 2z + z = 180
• 6z = 180
• z = 30
- Now x would be 90 and y would be 60
- The longest side would be the side opposite to the largest angle so longest side must be YZ .
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