If a triangle has sides \(a, b, c\), and fixed sum \(a + b + c = 18\), then the maximum possible area (in \(\text{cm}^2\)) of the triangle is
\(9\sqrt{3}\)
For a fixed perimeter, area is maximised by an equilateral triangle.
Side = 18/3 = 6 → Area = (√3/4)·6² = 9√3 cm².
Important Questions from Mensuration
The areas of three adjacent faces of a cuboidal tank are 3 m 2, 12 m 2 and 16 m 2. the capacity of the tank, in litres, is:
Volume of a cuboid is 4800 cm 3. If the height of this cuboid is 20 cm, then what will be the area of the base of cuboid ?
Two similar cubes have heights of 8 cm and 12 cm, respectively. If the capacity of the smaller cube is 80 cm 3, what is the capacity of the bigger cube (in cm 3)?
Three circles of radius 7 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string?
Three circles of radius 6 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string?
