Question

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

Answer 1

Length short if I walk diagonally across the park rather than along two sides of it = 1 mile

Explanation:

Given:

Shape of park is a rectangle

Length of park =2 miles

Width of park = 1.5 miles

Walking path is diagonally across the park.

So, we need to find length of diagonal of the park.

The diagonal of a rectangle cuts the rectangle into two right triangles as all angles of a rectangle is at right angles. So, we can apply Pythagorean theorem to find the diagonal of the rectangle.

Applying Pythagorean theorem [
`c^2=a^2+b^2` ]

For the rectangle,

`d^2=l^2+w^2`

where
`d` represents length of diagonal

`l` represents length of park

`w` represents width of park

Substituting values.

`d^2=(2)^2+(1.5)^2`

`d^2=4+2.25`

`d^2=6.25`

Taking square root both sides to find
`d`.

`√(d^2)=√(6.25)`

`d=2.5` miles.

So, length of my walk = 2.5 miles

Length along two sides of the park =
`2+1.5=3.5` miles

Length short if I walk diagonally across the park rather than along two sides of it =
`3.5-2.5 =1` mile (Answer)