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

As the park is rectangular, all the angles are 90^∘ In right angled Δ ABC, AC^2 = AB^2 + BC^2 nbsp; nbsp; nbsp; nbsp; [by Pythagoras theorem] ⇒ AC^2 ...

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Standard IX

Mathematics

Pythagoras Theorem

Jayanti takes...

Question

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

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Solution

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

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

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

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