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
A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are Big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted?
A and B are two heavy steel blocks. If B is placed on the top of A, the weight increases by 60%. How much weight will reduce with respect to the total weight of A and B, if B is removed from the top of A?
A gardener increased the area of his rectangular garden by increasing its length by 40% and decreasing its width by 20%. The area of the new garden
A village having a population of 4000 requires 150 liters of water per head per day. It has a tank measuring 20 m x 15 m x 6 m. The water of this tank will last for
The centroid of an equilateral triangle ABC is G. If AB is 6 cms, the length of AG is
