If in a triangle the circumcentre, incentre, centroid and orthocentre are at the same place, then what will that triangle be like?

A rectangular LCD has an area of 480 $${{cm^2}}$$ and a perimeter of 92 $${{cm^2}}$$ . If the size of the LCD is defined of the diagonal, then what the size of the LCD?

A circle touches all four sides of a quadrilateral ABCD. If AB = 18 cm, BC = 21 cm and  = 15 cm, then length CD is: 

The perimeter of a square is equal to the perimeter of a rectangle, and the latter has a width of 12 cm. The area of the square is 400 cm² . Find the area of the rectangle.

The length and the breadth of a rectangle are made to increase and decrease, respectively, by 8% and 10%. What is the percentage increase or decrease in its area?

Length of rectangle is 80% of diagonal of square of area 1225, then find area of rectangle if it's perimeter is 94√2.

The length of a plot is five times its breadth. A playground measuring 245 square metres occupies half of the total area of the plot. What is the length of the plot?

A prism and a pyramid have the same base and the same height. Find the ratio of the volumes of the prism and the pyramid.