question_answer

A rectangular carpet has an area of \[120\text{ }{{m}^{2}}\] and a perimeter of 46 m. The length of its diagonal is

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 \[=\sqrt{{{a}^{2}}+{{b}^{2}}}=\sqrt{{{15}^{2}}+{{8}^{2}}}=17\,m.\]