Question

The given figure shows a triangle PQR in which XY is parallel to QR. If PX : XQ = 1 : 3 and QR = 9 cm, find the length of XY.
Further, if the area of $\Delta$ PXY = x $c{m}^2$; find, in terms of x, the area of : (i) triangle PQR. (ii) trapezium XQRY.

Answer 1

PX/QX=1/3
on reversing ,
QX/PX+1=3+1
PQ/PX=4
PQ/PX=QR/XY
QR/XY=4
9=4XY
XY=9/4

2)$△$PXY is similar to $△$PQR

Area of PQR = 16x

Area of XQRY= 16x-x = 15x