Question

A rectangular piece of land whose length is twice its width has a diagonal distance of 80 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 its​ width?

Answer 1

Answer:

27.4 yards

Explanation:

The diagonal of a rectangle, one of it's length and one of it's width will form a right angle triangle

Let

Width = x

Length = 2x

Diagonal = 80 yards

c^2 = a^2 + b^2

Where

c= diagonal

a= length

b= width

c^2 = a^2 + b^2

80^2 = (2x)^2 + (x)^2

80^2 = 2x * 2x + x^2

80^2 = 4x^2 + x^2

6,400= 5x^2

Divide both sides by 5

x^2= 6400 / 5

= 1280

x^2 = 1,280

Find the square root of both sides

√x^2 = √1,280

x= 35.8

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 its​ width?

Yards saved= (Length + width) - diagonal

= (2x+x) - 80

= {2(35.8) + 35.8} - 80

= (71.6 + 35.8) - 80

= 107.4 - 80

= 27.4

Yards saved = 27.4 yards