10th Class Mathematics Coordinate Geometry Question Bank Case Based (MCQs) - Coordinate Geometry

The perimeter of \[\Delta PQR\] is:

A) \[(\sqrt{10}+5+3\sqrt{5})\] units

B) \[(\sqrt{10}+8\sqrt{5})\] units

C) \[(10+3\sqrt{5})\] units

D) \[(\sqrt{10}+5\sqrt{3})\] units

Correct Answer: A

Solution :

Length of PQ

\[=\sqrt{{{(4-1)}^{2}}+{{(6-5)}^{2}}}=\sqrt{{{(3)}^{2}}+{{(1)}^{2}}}\]

\[=\sqrt{9+1}=\sqrt{10}\] units.

Length of QR

\[=\sqrt{{{(7-4)}^{2}}+{{(2-6)}^{2}}}=\sqrt{{{(3)}^{2}}+{{(-4)}^{2}}}\]

\[=\sqrt{9+16}=\sqrt{25}=5\]units.

and Length of RP

\[=\sqrt{{{(1-7)}^{2}}+{{(5-2)}^{2}}}=\sqrt{{{(-6)}^{2}}+{{(3)}^{2}}}=\sqrt{36+9}\]

\[=\sqrt{45}=3\sqrt{5}\]units

\[\therefore \] Perimeter of \[\Delta PQR\]

\[=PQ+QR+RP=(\sqrt{10}+5+3\sqrt{5)}\]units.

So, option [a] is correct,