Question

​Ques:- adjacent sides of a rectangle are in the ratio 5:12 if the perimeter of the rectangle is 34 cm find the lenght of its diagonal. r v going to do this ques by pythagoras theorom.​

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{ABCD}\mathrm{be}\mathrm{the}\mathrm{rectangle}. \\ \mathrm{Let}\mathrm{the}\mathrm{breadth}\mathrm{of}\mathrm{the}\mathrm{rectangle},\mathrm{BC}=5\mathrm{x}\mathrm{cm} \\ \mathrm{then}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{rectangle},\mathrm{AB}=12\mathrm{x}\mathrm{cm} \\ \mathrm{Now},\mathrm{perimeter}=34\mathrm{cm} \\ \Rightarrow 2\left(\mathrm{length}+\mathrm{breadth}\right)=34 \\ \Rightarrow 12\mathrm{x}+5\mathrm{x}=17 \\ \Rightarrow 17\mathrm{x}=17 \\ \Rightarrow \mathrm{x}=1 \\ \mathrm{So},\mathrm{length}=12\mathrm{cm};\mathrm{breadth}=5\mathrm{cm} \\ \mathrm{We}\mathrm{know}\mathrm{that}\mathrm{each}\mathrm{angle}\mathrm{of}\mathrm{rectangle}\mathrm{is}\mathrm{a}\mathrm{right}\mathrm{angle}. \\ \mathrm{So},\angle \mathrm{B}=90°. \\ \mathrm{In}∆\mathrm{ABC}, \\ {\mathrm{AC}}^2={\mathrm{AB}}^2+{\mathrm{BC}}^2\mathbf{}\left[\mathbf{Pythagoras}\mathbf{}\mathbf{Theorem}\right] \\ \Rightarrow {\mathrm{AC}}^2={\left(12\right)}^2+{\left(5\right)}^2 \\ \Rightarrow {\mathrm{AC}}^2=144+25 \\ \Rightarrow {\mathrm{AC}}^2=169 \\ \Rightarrow \mathrm{AC}=13\mathrm{cm} \\ \mathrm{So},\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{diagonal}\mathrm{of}\mathrm{rectangle}\mathrm{ABCD}=13\mathrm{cm} \end{gathered}$$