Question

In a rectangle ABCD if X and Y are the midpoints of sides AB and BC respectively, find the ratio of the area of triangle DXY and that of the rectangle?​

Answer 1

Given: In a rectangle ABCD if X and Y are the midpoints of sides AB and BC respectively.

To find:  The ratio of the area of triangle DXY and that of the rectangle ?

Solution:

• Let the length of rectangle be n and breadth be m.

                     Now area of rectangle ABCD = mn

                     area of triangle DCY = 1/2 x n x m/2 = mn/4

                     area of triangle DAX = 1/2 x n/2 x m = mn/4

                     area of triangle XBY = 1/2 x n/2 x m/2 = mn/8

• Now area of triangle DXY =  area of rectangle ABCD - (area of triangle DCY + area of triangle DAX + area of triangle XBY )

                     area of triangle DXY = mn - (mn/4 + mn/4 + mn/8)

                     area of triangle DXY = mn - mn/2 - mn/8

                     area of triangle DXY = mn/2 - mn/8

                     area of triangle DXY = mn(8-2/16)

                     area of triangle DXY = 6mn / 16

• Now the ratio of the area of triangle DXY and that of the rectangle is:

                     6mn / 16  /  mn

                     6/16

                     3/8

• So the ratio is 3:8.

Answer:

                   So the ratio of the area of triangle DXY and that of the rectangle is: 3:8