Question

In triangle pqr, x and y are points on pq and pr such that xy||qr. If px = 4 cm, xq = 6 cm and yr = 8 cm. Find py?

Answer 1

Answer:

$PY=\frac{16}{3}$

Step-by-step explanation:

It is given that PQR is a triangle and X and Y are the points on the sides PQ and PR respectively, and PX=4cm, XQ=6cm and YR=8cm.

Since, XY is parallel to QR, thus the triangle PXY is similar to triangle PQR, hence using the basic proportionality theorem, we get

$\frac{PX}{PQ}=\frac{PY}{PR}$

Substituting the given values, we have

$\frac{4}{10}=\frac{PY}{PY+8}$

$\frac{2}{5}=\frac{PY}{PY+8}$

$2PY+16=5PY$

$16=3PY$

$PY=\frac{16}{3}$

Thus, the value of PY is ${\frac{16}{3}$.