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