Kimi's school is $15$ kilometers west of her house and $8$ kilometers south of her friend Franklin's house. Every day, Kimi bicycles from her house to her school. After school, she bicycles from her school to Franklin's house. Before dinner, she bicycles home on a bike path that goes straight from Franklin's house to her own house. How far does Kimi bicycle each day? $\newline$ $\_\_\_\_\_$ kilometers

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Pythagorean Theorem and its converse

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Q. Kimi's school is

15

kilometers west of her house and

8

kilometers south of her friend Franklin's house. Every day, Kimi bicycles from her house to her school. After school, she bicycles from her school to Franklin's house. Before dinner, she bicycles home on a bike path that goes straight from Franklin's house to her own house. How far does Kimi bicycle each day?

\newline

\_\_\_\_\_

kilometers

Calculate Distance Kimi-School: Calculate distance from Kimi's house to school. $\newline$ Distance = $15\,\text{km}$ .
Calculate Distance School-Franklin: Calculate distance from school to Franklin's house. $\newline$ Distance = $8\,\text{km}$ .
Use Pythagorean Theorem: Use Pythagorean Theorem to find distance from Franklin's house to Kimi's house. $a^2 + b^2 = c^2$ , where $a = 15\,\text{km}$ , $b = 8\,\text{km}$ . $15^2 + 8^2 = c^2$ .
Perform Calculation: Perform the calculation. $\newline$ $225 + 64 = c^2$ . $\newline$ $289 = c^2$ .
Find Square Root: Find the square root of $289$ . $\newline$ $c = \sqrt{289}$ . $\newline$ $c = 17 \, \text{km}.$
Add Total Distance: Add up all distances to find total distance Kimi bicycles. $\newline$ Total distance = $15\,\text{km} + 8\,\text{km} + 17\,\text{km}$ . $\newline$ Total distance = $40\,\text{km}$ .