2023 · Q88
The perimeter and the area of a right-angled triangle are 36 cm and 54 square cm respectively. What is the length of the hypotenuse?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A12 cm
- B14 cm
- C15 cm
- D16 cm
Explanation
Let the legs be a, b and hypotenuse c: a + b + c = 36 and ab/2 = 54, so ab = 108. Then c² = a² + b² = (a + b)² − 2ab = (36 − c)² − 216. Expanding gives 72c = 1080, so c = 15 cm (C).