The value of $$\frac{[(34.45)]^2-(11.75)^2]×5.15}{[(25.75)^2+(25.75×20.45)]×22.7}$$​ is:

Correct option is A

Given:

​$$\frac{[(34.45)^2-(11.75)^2]×5.15}{[(25.75)^2+(25.75×20.45)]×22.7}$$​​

Formula Used:

​$$\begin {array}{|c|c|} \hline \textbf{Operation preference wise} & \textbf{Symbol} \\ \hline Brackets &[],{}, () \\ \hline Orders, of & ² (power), √ (root) , of \\ \hline Division & ÷ \\ \hline Multiplication & × \\ \hline Addition & + \\ \hline Subtraction & - \\ \hline \end{array}$$​

Solution:

​$$\frac{[(34.45)^2-(11.75)^2]×5.15}{[(25.75)^2+(25.75×20.45)]×22.7}$$​​

​$$=\frac{[(34.45+11.75)(34.45-11.75)]×5.15}{[(25.75)(25.75+20.45)]×22.7}$$​​

​$$=\frac{[(46.2)(22.7)]×5.15}{[(25.75)(46.2)]×22.7}$$​​

​$$=\frac{5.15}{25.75}$$​​

​$$=\frac{515}{2575}$$​​

​$$=\frac{515}{2575}$$​​

​$$= \frac{1}{5}$$​​