Question

Observe the figure given.
In $△PQR$, if $XY//PQ,\frac{PX}{XR}=\frac{5}{3}$ and $QR=7.2cm$, then find the length of $RY$.

Answer 1

Given that:

In $△PQR,XY\parallel PQ,\frac{PX}{XR}=\frac{5}{3}$ and $QR=7.2cm$

To find: $RY=?$

Solution:

In $△RXY$ and $△RPQ,$

Since, $XY\parallel PQ$

$\therefore △RXY\sim △RPQ$

So, $\frac{PR}{XR}=\frac{QR}{YR}$ $-------\left(i\right)$

Since, $\frac{PX}{XR}=\frac{5}{3}$

So, $\frac{PX}{XR}+1=\frac{5}{3}+1$

or, $\frac{PX+XR}{XR}=\frac{5+3}{3}$

or, $\frac{PR}{XR}=\frac{8}{3}$ $-------\left(ii\right)$

Now,$\frac{PR}{XR}=\frac{QR}{YR}$ (from eqn.$\left(i\right)$)

or, $\frac{QR}{YR}=\frac{8}{3}$ (from eqn.$\left(ii\right)$)

or, $YR=QR\times \frac{3}{8}$

or, $YR=7.2cm\times \frac{3}{8}$

or, $YR=2.7cm$

or, $RY=2.7cm$