2021 · Q11
The sides of a right-angled triangle are in the ratio x ∶ (x − 1) ∶ (x − 18). What is the perimeter of the triangle?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A28 units
- B42 units
- C56 units
- D84 units
Explanation
Let the hypotenuse be x (the largest side). Then x² = (x−1)² + (x−18)², giving x² − 38x + 325 = 0, so x = 25 or x = 13. x = 13 would make the third side x − 18 = −5, impossible; x = 25 gives sides 7, 24, 25, and indeed 7² + 24² = 25². The perimeter is 7 + 24 + 25 = 56. Hence option C.