Question

Jayanti takes shortest route to her home by walking diagonally across a rectangular park. The park measures $60m\times 80m$. How much shorter is the route across park than the route around its edges?

Answer 1

As the park is rectangular, all the angles are ${90}^{\circ }$

In right angled $\Delta ABC$, $A{C}^2=A{B}^2+B{C}^2$ [by Pythagoras theorem]
$\Rightarrow A{C}^2=(60{)}^2+(80{)}^2=3,600+6,400\Rightarrow A{C}^2=10,000\Rightarrow AC=\sqrt{10,000}\Rightarrow AC=100m$
If she goes through AB and AC, then total distance covered = (60 + 80) m = 140 m
$\therefore$ Difference between two paths = (140 - 100) m = 40 m