2020 · Q82
The lengths of sides of triangle are 3x, 4√y, 5∛z, where 3x < 4√y < 5∛z. If one of the angles is 90°, then what are the minimum integral values of x, y, z respectively?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A1, 2, 3
- B2, 3, 4
- C1, 1, 1
- D3, 4, 5
Explanation
Being right-angled with 3x < 4√y < 5³√z, the hypotenuse is 5³√z: 9x² + 16y = 25z²ʳ. The smallest positive integers satisfying this with the strict ordering are x = y = z = 1 (9 + 16 = 25 and 3 < 4 < 5). No smaller positive integers can satisfy 9x² + 16y = 25z²ʳ.