2024 · Q49
The base of a right-angled triangle is 4/3 times the height of triangle. If the area of the triangle is 54 square cm, then what is the perimeter of the triangle?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A30 cm
- B32 cm
- C36 cm
- D40 cm
Explanation
Let the height be h; then the base is 4h/3. Area = ½ × (4h/3) × h = 2h²/3 = 54, so h² = 81 and h = 9 cm. Then base = 12 cm and hypotenuse = √(81+144) = 15 cm. The perimeter is 9 + 12 + 15 = 36 cm — option C.