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?

1 Answer
Oscar L.
Feb 27, 2017

The other two sides each have a maximum length of #14# centimeters.

Explanation:

In an obtuse triangle, the square of the longest side is greater than the sum of squares of the other two sides. So the equal legs must have a length #L# such that #L^2+L^2=2L^2# must be less than #(20"cm")^2=400"cm"^2#. The largest whole number #L# that works is #14"cm"#.

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