A rectangle is a quadrilateral in which all the four angles are right angles and the opposite sides are equal in length.

Let be a rectangle having and . Let be the diagonal which divides the rectangle into two right triangles, and .

__Example__:

In exchange for a square plot of land, one of whose sides is m, a man wants to buy a rectangular plot m long which is of the same area as the square plot. Find the width of the rectangular plot.

__Solution__:

Side of the square plot m

Area of the square plot square m

Length of the rectangular plot m

Length of the rectangular plot area of square plot

Length of the rectangular plot Square m

Width of rectangular plot m

__Example__:

How many tiles cm square will be required to pave a footpath m wide carried round the outside of a grassy plot m long and m broad.

__Solution__:** **

Width of foot path m

Outside dimensions of the plot are m and m

Now,

Outside area of plot square m

Inside area of plot square m

Area of foot path outside area inside area square m

Area of one tile square m

Number of tiles required tiles