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
In a circular garden of radius 15 m, a path of 2 m wide has to be made inside the garden at the rate of ₹ 24 per sq. m. The cost of making the path is: (Take π = \(\frac{22}{7}\) )
A hollow cylinder with outer radius 4 cm and height 2 cm is made up of 1 cm thick metal sheet. What is the volume of metal used? (Take π = \(\frac{22}{7}\))
The length and breadth of a rectangular field are in the ratio 4 : 3. If the cost of cultivating the field at ₹2 per m 2is ₹600, then the length of the field is:
A cylindrical tank has a capacity of 5632 m3. If the diameter of its base is 8 m, what is the depth of the cylindrical tank? (Use π = \(\frac{22}{7}\))
Find the surface area of a sphere whose diameter is equal to 28 cm.
