An employee is walking home from work and wants to take the long way to get more exercise. The diagram represents the two
different routes, where A is the employee's work and B is the employee's home. Which route is longer and by how much? will mark brainliest

Answer:

The route from A to the corner to B is longer then going directly from A to B. It is roughly 1.6 miles longer.

Step-by-step explanation:

The distance from A to the corner to B is 5.9 miles because

[tex]3.8 + 2.1 = 5.9[/tex]

Going directly from A to B is roughly 4.3 miles because of

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

[tex]5.9 - 4.3 = 1.6[/tex]

Answer:

Walking to the right and downwards to reach B from A.

Approximately [tex]1.6[/tex] miles.

Step-by-step explanation:

Route 1 - Walking to the right and downwards to reach B from A:

The distance is [tex]2.1+3.8=5.9[/tex] miles

Route 2 - Walking straight to B from A:

[tex]\sqrt{3.8^2+2.1^2} = \sqrt{14.44+4.41}[/tex] (using the Pythagorean theorem, the two lengths are perpendicular)

[tex]=\sqrt{18.85}[/tex]

[tex]=4.341658669[/tex] miles (approximately from calculator)

Since [tex]5.9[/tex] miles is greater than [tex]4.341658669[/tex] miles, therefore walking to the right and downwards to reach home from work is the longest distance.

Difference in distance:

[tex]5.9-4.341658669=1.558341331[/tex] miles

Route 1 is longer than route 2 by [tex]1.558341331[/tex] miles, or approximately [tex]1.6[/tex] miles.

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