Question

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

Explanation:

Step1: Apply the Pythagorean - like inequality for obtuse - angled triangles

For an isosceles triangle with side lengths \(a\), \(a\), and \(c\) (\(c\) is the longest side), in an obtuse - angled triangle, \(a^{2}+a^{2}

Step2: Solve for \(a\)

Taking the square - root of both sides of \(a^{2}<200\), we get \(a < \sqrt{200}\). Since \(\sqrt{200}\approx14.14\).

Step3: Find the greatest whole - number value

The greatest whole - number less than \(14.14\) is \(14\).

Answer:

C. 14 cm