A rectangle park has a diagonal path AC. The length of the park is 12 m and its width is 5 m. Which route is shorter AB + BC or AC and by how much?

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Solution

In the given figure
The length of Park is $12 m$ and its Width is $5 m \Rightarrow 12 + 5 = 17$
If you travel diagonally through AC your distance will be shorter
To find out the diagonally AC you have to apply $P y t h a g o r e a n t h e o r e m$ which is

$\begin{matrix} h y p o t e n u s e^{2} = b a s e^{2} + h e i g h t^{2} [h y p o t e n u s e = A C, b a s e = A B, h e i g h t = B C] A C^{2} = A B^{2} + B C^{2} A C^{2} = 12^{2} + 5^{2} A C^{2} = 144 + 25 = 169 A C = \sqrt{169} = \sqrt{13 \times 13} = 13 m n o w s e e 13 m < 17 m s o i f y o u g o d i a g o n a l l y t h r o u g h A C y o u r d i s t a n c e b e s h o r t e r b y (17 m - 13 m) = 4 m . . . A n s \end{matrix}$

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