Question

On Monday, Amie rides her bike from home to school. After school, she bikes to work. After work, she bikes home. Based on the information in the diagram below, about how many miles does Amie bike on Monday?

10.9 mi.
11.3 mi.
12.7 mi.
13.1 mi.

Answer 1

The correct option is D. 13.1 miles

Explanation:

Distance from school to home = 2.5 miles

Distance from Home to work = 4.5 miles

Now, The distance of school to work can be calculated by using law of cosines in the triangle

Let Distance from school to work be x miles

Now, using law of cosine :

⇒ x² = 2.5² + 4.5² - 2 × 2.5 × 4.5 × cos 120°

⇒ x² = 37.75

⇒ x = 6.14

So, Distance of school to the work = 6.14 miles

Now, miles traveled by Amie bike on Monday = 2.5 + 6.14 + 4.5

= 13.14 miles

Therefore, The correct option is D. 13.1 miles

Answer 2

Let the distance between the school and work = d //
Using the cosine law to find d //

d² = 4.5² + 2.5² - 2 *2.5 *4.5 cos 120 = 37.75 // ∴ d = √37.75 = 6.14
∴ Total distance = 6.14 + 2.5 + 4.5 = 13.14
The correct choice is the fourth option ⇒⇒⇒⇒ 13.1 mi