Question
In the figure, given below, PQR is a right-angle triangle right angled at Q. XY is parallel to QR, PQ = 6 cm, PY = 4 cm and PX : XQ = 1 : 2. Calculate the lengths of PR and QR.
✓
Answer
Given that $\frac{P X}{X Q}=\frac{1}{2}$ and $XY \| QR$
So, $\frac{P X}{X Q}=\frac{P Y}{Y R}=\frac{1}{2}$
Since PY = 4cm, YR = 8cm.
Hence, PR = 12 cm
Since ΔPQR is a right-angled triangle
By Pythagoras theorem,
$Q R^2=P R^2-P Q^2$
$\Rightarrow Q R^2=12^2-6^2$
$\Rightarrow Q R^2=144-36$
$\Rightarrow Q R^2=108$
$\Rightarrow QR =10.39 cm$
So, $\frac{P X}{X Q}=\frac{P Y}{Y R}=\frac{1}{2}$
Since PY = 4cm, YR = 8cm.
Hence, PR = 12 cm
Since ΔPQR is a right-angled triangle
By Pythagoras theorem,
$Q R^2=P R^2-P Q^2$
$\Rightarrow Q R^2=12^2-6^2$
$\Rightarrow Q R^2=144-36$
$\Rightarrow Q R^2=108$
$\Rightarrow QR =10.39 cm$
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