A) 15 m
B) 16 m
C) 17 m
D) 20 m
Correct Answer: C
Solution :
Let the sides be a and b as shown in figure Area\[=ab=120\] ...(1) Perimeter\[=2\left( a+b \right)=46\] \[\Rightarrow a+b=23\] ?(2) We have \[{{(a-b)}^{2}}={{(a+b)}^{2}}-4ab\] \[\therefore \]\[a-b=\sqrt{{{(23)}^{2}}-4\times 120}=7\] ?(3) Solving (2) and (3), we get \[a=15,b=8\] \[\therefore \] The length of diagonal of the carpet \[=\sqrt{{{a}^{2}}+{{b}^{2}}}=\sqrt{{{15}^{2}}+{{8}^{2}}}=17\,m.\]You need to login to perform this action.
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