Question

Which dimensions cannot create a triangle?
three angles measuring 25 degrees, 65 degrees, and 90 degrees
three angles measuring 50 degrees, 30 degrees, and 100 degrees
three sides measuring 5 in., 12 in., and 13 in.
three sides measuring 4 ft, 8 ft, and 14 ft

Answer 1

Only the sides 4 ft, 8 ft, and 14 ft cannot form a triangle.

Reason:
- Angle sets: 25°+65°+90° = 180° and 50°+30°+100° = 180°, so both are valid triangle angle sets.
- Sides 5, 12, 13 satisfy the triangle inequalities (and 5^2+12^2=13^2, a right triangle).
- For 4, 8, 14: 4 + 8 = 12 ≤ 14, so the sum of two sides is not greater than the third; therefore no triangle can be formed.