A) 5 units
B) 3 units
C) \[\sqrt{34}\]units
D) A units
Correct Answer: C
Solution :
Now, length of the diagonal AB = Distance between the points A(0, 3) and B(5, 0). |
\[\because\] Distance between the points\[\left( {{x}_{1}},\,{{y}_{1}} \right)\] and \[\left( {{x}_{2}},\,{{y}_{2}} \right)\], |
\[d=\sqrt{{{\left( {{x}_{2}}-{{x}_{1}} \right)}^{2}}+{{\left( {{y}_{2}}-{{y}_{1}} \right)}^{2}}}\] |
Here, \[{{x}_{1}}=0,\] \[{{y}_{1}}=3\]and \[{{x}_{2}}=5,\,{{y}_{2}}=0\] |
\[\therefore\] Distance between the points \[A\left( 0,\,3 \right)\]and B (5,0) |
\[AB=\sqrt{{{\left( 5-0 \right)}^{2}}+{{\left( 0-3 \right)}^{2}}}\] |
\[=\sqrt{25+9}=\sqrt{34}\] |
Hence, the required length of its diagonal is \[\sqrt{34}\] units. |
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