A) 16 m
B) 17 m
C) 18 m
D) 20 m
E) None of these
Correct Answer: B
Solution :
Explanation Rectangular area \[=\,\,\ell \,\,\times b = 120\] and perimeter \[\Rightarrow \,\,\,\,\,\,\ell +b = 23\] \[\Rightarrow \,\,\,\,\,\,\ell +b = 23\] ........ (i) Now, \[{{(\ell -b)}^{2}}-\,\,4\,\ell b\,\,=\,\,{{(23)}^{2}}\,\,-\,\,4\,\,\times \,\,120\,\,=\] \[(529-480)\,\,=\,\,49\,\,\,\Rightarrow \,\,\,\ell -b=7\] ........ (ii) On solving equation (i) and (ii), we get \[\ell =15, b = 8\] Diagonal \[=\,\,\sqrt{{{15}^{2}}+{{8}^{2}}}\,\,=\,\,\sqrt{225+64}\,\,=\,\,\sqrt{289}\,\,=\,\,17m.\]
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