Question

in triangle PQR .a line joining point X on side PQ and point Y on side PR parallel to side QR .if the ratio of PY:YR is 3:5 and the length PX=7cms then the length of the side PQ is​

Answer 1

Step-by-step explanation:

Given that,

In triangle PQR, a line joining point X on side PQ and point Y on side PR parallel to side QR . If the ratio of PY:YR is 3:5 and the length PX=7cm.

Then,

In triangle PQR and PXY,

∠PQR =∠PXY (PQ//XY,being corresponding angle)

∠PRQ =∠PYX (PQ//XY,being corresponding angle)

∠QPR =∠XPY (common angle)

So, △PQR ~ △PXY ( ~ means similarity)

Sides of the similar triangles are in proportional

Then,

PQ = PR = QR

PX PY XY

i.e. PQ = PY+YR = QR

PX PY XY

Taking 1st and 2nd ratios

PQ = PR

PX PY

or, PQ/7 = (3+5)/3

or, PQ = 8/3 * 7

i.e. PQ = 56/3cm = 18.67cm

Answer 2

Answer:

see the image it will be helpful for you