2025 · Q53
Consider the following for the next two (02) items that follow: ABC is a triangle right-angled at B. The perimeter of the triangle is 24 cm, and the difference between the sum of the perpendicular sides and the hypotenuse is 4 cm. What is the area of the triangle ABC?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A18 square cm
- B24 square cm
- C36 square cm
- D48 square cm
Explanation
Let the perpendicular sides be a, c and hypotenuse b: a + c + b = 24 and (a+c) − b = 4 give a + c = 14, b = 10. Then a² + c² = 100 and (a+c)² = 196 give 2ac = 96, so ac = 48. Area = ac/2 = 24 cm², option (b).