2018 · Q89
If ABC is a right-angled triangle with AC as its hypotenuse, then which one of the following is correct?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AAC³ = AB³ + BC³
- BAC³ > AB³ + BC³
- CAC³ ≤ AB³ + BC³
- DAC³ ≥ AB³ + BC³
Explanation
AC^2 = AB^2 + BC^2 gives AC^3 = AC x AB^2 + AC x BC^2. Since the hypotenuse AC exceeds each leg, AC x AB^2 > AB^3 and AC x BC^2 > BC^3. So AC^3 > AB^3 + BC^3. Hence option B.