A rectangular brick is kept on a table with a part of its length projecting out. It remains at rest if thelength projected is slightly less than half the total length but it falls down if the length projected is slightly more than half the total length. Give reason.

Half the perimeter of a rectanguler garden id 36m. If the length is 4m more than its width. Find the dimensions of the garden.

A rectangular park is to be designed whose breadth is 3 m less than its length. Its area is to be 4 square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude 12 m. Find its length and breadth.

Figure shows a smooth track which consists of a straight inclined part of length l joining smoothly with the circular part. A particle of mass m is projected up the incline from its bottom. a.Find the minimum projected speed v_0 for which the particle reaches the top of the track. b. Assuming that the projection speed is 2v_0 and that the block does not lose contact with the track before reading its top, find teh force acting on it whenit reaches the top. c. Assuming that teh projection speed is only slightly greater than v_0 where will the block lose contact with the track?

Represent the following situations in the form of quadratic equation: The area of a rectangular plot is 528 m^(2) . The length of the plot is one metre more than twice its breadth. We need to find the length and breadth of the plot.