Question

1. In Fig. 12.97, in A PQR if XY || QR, PX = 1 cm, XQ = 3 cm, YR = 4:5 cm and QR = 9 cm, find (i) PY and (ii) XY. Further, if the area of the APXY is A cm2, find in terms of A, (iii) the area of the triangle PQR (iv) the area of the figure XYRQ.​

Answer 1

Answer:

From the figure,

XY || QR, PX = 1cm, QX = 3cm, Y R = 4.5cm

and QR = 9cm,

So, PX/QX = PY/YR

1/3 = PY/4.5

By cross multiplication we get,

(4.5 x 1)/3 = PY

PY = 45/30

PY = 1.5

Then, /_ X = /_ Q

/_Y = /_R

So, /_ PXY ~ triangle R

Therefore, XY/QR = PX/PQ

XY /9 = 1/(1+3)

XY/9 = 1/4

XY = 9/4

XY = 2.25.