question_answer

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

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