A rectangular sheet of paper has area 24 sq. meters. The margin
at the top and at the bottom are 75 cm each and at the sides 50 cm
each. What are the dimensions of the paper, if the area of the
printed space is maximum?

The perimeter of a triangle is 10 cm. If one of the side is 4 cm. What are the other two sides of the triangle for its maximum area?

An oil funnel of tin sheet consists of a cylindrical portion 10 cm long attached to a frustum of cone. The diameters of the top and bottom of the frustum are 18 cm and 8 cm respecti8vely. If the slant height of the frustum of the cone is 13 cm, find the area of the tin required to make the funnel from the given information in the figure (pi=3.14)

A rectangular Sheet of paper of fixed perimeter with the sides having their length in the ratio 8:15 converted in to an open rectangular box by folding after removing the squares of equal area from all corners. If the total area of the removed squares is 100, the resulting box has maximum volume. Find the lengths of the rectangular sheet of paper.

A box with a square base is to have an open top. The surface area of the box is 192 sq.cm. What should be its dimensions in order that the volume is largest?

The product of the lengths of the sides forming a right angle of a right angled triangle si 50 cm^2 . What is the area of this triangle ?