Question

An employee is walking home from work and wants to take the long way to get more exercise. The diagram represents the two

Answer 1

Answer:

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

Approximately $1.6$ miles.

Step-by-step explanation:

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

The distance is $2.1+3.8=5.9$ miles

Route 2 - Walking straight to B from A:

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

$=\sqrt{18.85}$

$=4.341658669$ miles (approximately from calculator)

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

Difference in distance:

$5.9-4.341658669=1.558341331$ miles

Route 1 is longer than route 2 by $1.558341331$ miles, or approximately $1.6$ miles.

Answer 2

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

$3.8 + 2.1 = 5.9$

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

${a}^{2} + {b}^{2} = {c}^{2}$

$5.9 - 4.3 = 1.6$