A park is in the shape of a rectangle 2 miles long and 1.5 miles wide. How much shorter if you walk diaganolly across the park rather than along two sides?

You can answer this by using Pythagoras theorem. Okay, let me draw this first.

2 miles
V
________________________
|                                        |
|                                        |
|                                        |   << 1.5 miles
|_______________________|

^ Assume this is the rectangle. The long side is 2 miles while the shorter side is 1.5 miles.

So, to get the shortest distance, let’s cut out a triangle from the rectangle.

/|
/  |
/    |
What we want to find is this one >  /      |  << 2 miles
/        |
/______|
^ 1.5 miles (I know the size is not logical, but imagine                                                                       it please)

So to get the diagonal length = $$\sqrt{{a^{2} }+ b^{2}}$$
=  $$\sqrt{{2^{2} }+ 1.5^{2}}$$
=  2.5 miles

To calculate how much shorter = ( 2 miles + 1.5 miles) - 2.5 miles
= 3.5 miles - 2.5 miles
= 1.0 miles

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