9th ncert solution Ch area of parallelogram and triangle optional exercise

1.Parallelogram ABCD and rectangle ABEF are on the same base AB and have equal areas. Show that the perimeter of the parallelogram is greater than that of the rectangle.

Solution. IIgm ABCD and rectangle ABEF are between the same parallels AB and CF.

 AB = EF (For rectangle) and AB = CD (For parallelogram)

∴ CD = EF  ⇒ AB + CD = AB + EF ... (1)

Of all the line segments that can be drawn to a given line from a point not lying on it, the perpendicular line segment is the shortest.

∴ AF < AD

similarly we write , BE < BC          ∴ AF + BE < AD + BC ... (2)

From equations (1) and (2), we get

AB + EF + AF + BE < AD + BC + AB + CD
Perimeter of rectangle ABEF < Perimeter of parallelogram ABCD