The length breadth and height of a cuboidal room be a unit, b unit, and c unit respectively and a + b + c = 25, ab + bc +ca = 240.5 then find the length of the longest rod to be ket inside the room.

The length , breath and height of rectangular parallelopiped room are 5 m , 4 m and 3 m respectively. Find the length of the longest rod that can be put into that room.

The lengths of transverse and conjugate axes of a hyperbola are 4 unit and 6 unit respectively and their equations are x + 3 = 0 and y - 1 = 0, find the equation of the hyperbola.

The lengths of the diamensions of two cuboids are 4,6,4 units and 8,(2h-1), 2 units respectively, If the volumes of two cuboids are equal , then find the value of h.

Prove (a + b + c) (ab + bc + ca) > 9abc

If a + b + c = 8 and ab + bc + ca = 11 , then find the value of a^(3)+b^(3)+c^(3)-3abc

The length and breadth of vuboidal room are 20 metres and 16 metres respectively. The sum of the surface areas of the roof and of the floor of the room is equal to the surface areas of four walls of the room. Find the height and volume of the room.

If a + b +c =9 and ab + bc + ca =26, then find a ^(2) + b ^(2) + c ^(2).

Length of a side of a cube is 5 unit, find its total surface.

The length of two adjacent walls of a room are 12m and 8 m respectively. If the height of the room is 4m then find the area of the floor of the room.