Respuesta :
Answer:
Length short if I walk diagonally across the park rather than along two sides of it = 1 mile
Step-by-step 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 [ [tex]c^2=a^2+b^2[/tex] ]
For the rectangle,
[tex]d^2=l^2+w^2[/tex]
where [tex]d[/tex] represents length of diagonal
[tex]l[/tex] represents length of park
[tex]w[/tex] represents width of park
Substituting values.
[tex]d^2=(2)^2+(1.5)^2[/tex]
[tex]d^2=4+2.25[/tex]
[tex]d^2=6.25[/tex]
Taking square root both sides to find [tex]d[/tex].
[tex]\sqrt{d^2}=\sqrt{6.25}[/tex]
[tex]d=2.5[/tex] miles.
So, length of my walk = 2.5 miles
Length along two sides of the park = [tex]2+1.5=3.5[/tex] miles
Length short if I walk diagonally across the park rather than along two sides of it = [tex]3.5-2.5 =1[/tex] mile (Answer)
