Is it possible to design a rectangular mango grove whose length is twice its breadth, and area is 800 m²? If so, find its length and breadth.

A teacher on attempting to arrange the students for mass drill in the form of a solid square found that 24 students were left. When he increased the size of the square by one student, he found that lie was short of 25 students. Find the number of students.

The area of a triangle is 30 sq cm. Find the base if the altitude exceeds the base by 7 cm.

I want to design a rectangular park 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 breadth of the rectangular park and altitude 12 m. Is it possible to have such a rectangular park? If so, find its length and breadth.

A pole has to be erected at a point on the boundary of a circular park of diameter 13 meters in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Is it possible to do so? If yes, at what distances from the two gates should the pole be erected?