Word Problem. Help please!

Question

A rectangular piece of land whose length is twice it’s width has a diagonal distance of 60 yards. How many yards, to the nearest tenth of a yard, does a person save by walking diagonally across the land instead of walking its length and it’s with?

a person saves approximately___ yards.

Answer 1

x√5 = 60

x = 60 / √5

x = 26.8 yards

Walk around perimeter: 26.8 + 53.7

Walk directly = 60

Savings: 80.5 - 60 = 20.5 yards

Answer 2

call width w, then length is 2w.

By Pythagorean theorm w^2+(2w)^2 =(60)^2

5w^2= 3600

w^2= 720

w=26.83yds. Length then is 53.67yds

26.83 + 53.67=80.5 yds

so you save 20.5yds ( 60 instead of 80.5)

Answer 3

width = x

length = 2x

diagonal = 60 yards

First use the pythagorean theorem to solve for x:

(diagonal)² = (width)² + (length)²

diagonal = √((width)² + (length)²)

60 = √((x)² + (2x)²) = √(x² + 4x²) = √(5x²) = √(5) x

x = 60 / √(5)

Use x to solve for length and width:

length = 2x = 2* (60 / √(5)) = 120 / √(5) yards

width = x = 60 / √(5) yards

walking length and width = length + width = (120 / √(5) yards) + (60 / √(5) yards) = 180 / √(5) yards

walking diagonally = 60 yards

distance saved = (180 / √(5) yards) - 60 yards ≈ 20.5 yards