Question

In ΔXYZ , DE ║YZ , XD = 3cm , DY =2cm area of ΔXYZ = 10cm².Find the area of ΔXDE.

Answer 1

use similarly concept for triangle XDE and XYZ
angle YXZ=angle DXE
also DE|| YZ
hence ,
angle XYZ=angle XDE
and, angle XZY=angle XED
hence traingle XYZ similar triangle XDE
so,
XD/XY=XE/XZ=DE/zY=3/5
also if we drawn a perpendicular line from vertex X which cut DE at P and XY at Q
then triangle XDP and triangle XYQ also similar , in the same way
hence XD/XY=XP/XQ=3/5
now area of XYZ =1/2(YZ)(XQ)
area of XDE=1/2 (DE)(XP)

divided both ,
10/area of XDE=(YZ/DE)(XQ/XP)
=(5/3)(5/3)
=25/9
hence area of XDE=18/5 cm^2