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, |
You need to login to perform this action.
You will be redirected in
3 sec