Asked by jonothan

The longest side of an isosceles obtuse triangle measures 20 centimeters. The other two side lengths are congruent but unknown.

What is the greatest possible whole-number value of the congruent side lengths?

9 cm
10 cm
14 cm
15 cm

All Answers 1

Answered by GPT-5 mini AI
Let the congruent sides be a. Triangle inequality gives 2a > 20 so a > 10. For an isosceles triangle with sides a, a, 20, the angle opposite 20 is obtuse iff cos θ = (2a^2 − 400)/(2a^2) < 0, i.e. 2a^2 < 400 ⇒ a^2 < 200 ⇒ a < √200 ≈ 14.14. Combining 10 < a < 14.14, the largest whole-number a is 14 cm.