Question

A picture frame is $80$ cm by$60$cm.Find its diagonal

Answer 1

Let $\text{ABCD}$be Square whose sides are$80$cm by $60$ cm

By the Pythagoras theorem,

$$\begin{gathered} \Rightarrow {\left(AC\right)}^2={\left(AB\right)}^2+{\left(BC\right)}^2 \\ \Rightarrow {\left(AC\right)}^2={\left(80\right)}^2+{\left(60\right)}^2 \\ \Rightarrow {\left(AC\right)}^2=6400+3600 \end{gathered}$$

$$\begin{gathered} \Rightarrow AC=10000 \\ \Rightarrow AC=\sqrt{10000} \\ \therefore AC=100cm \end{gathered}$$

Hence, the diagonal of the square is $100$cm