2021 · Q17
If the perimeter of a right-angled triangle is 30 cm and the hypotenuse is 13 cm, then what is the area of the triangle?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A24 cm²
- B27 cm²
- C30 cm²
- D36 cm²
Explanation
Let the legs be a, b: a + b = 30 − 13 = 17 and a² + b² = 13² = 169. Then (a+b)² = a² + b² + 2ab gives 289 = 169 + 2ab, so ab = 60. The area is ab/2 = 30 cm². Hence option C.