Question

8. Each day, Amy walks to school. She leaves her home

and walks south 7 blocks to her friend's house. They then
turn to the west and walk 12 blocks to the school. At the
end of the day, Amy walks directly from the school to
her home.
a) To the nearest tenth (one decimal place), how many
blocks does Amy walk on her way home?
<+
-10
-10
Home s
-5
Friend's house
-5
-10
5
10
School
S
b) How many blocks does Amy walk in one day for her round trip to the school and back
home? Round to the nearest tenth.

Answer 1

13.9 blocks for a
32. 9 blocks for b
Explanation below

Answer 2

(a) 13.9 blocks (nearest tenth)

(b) 32.9 blocks (nearest tenth)

Explanation:

The given scenario can be modeled as a right triangle.

If Amy walks south 7 blocks, one leg of the triangle is 7.

If Amy then walks west 12 blocks, the other leg of the triangle is 12.

Part (a)

To calculate the number of blocks Amy walks on her way home if she walks directly from school to her home, find the length of the hypotenuse of the right triangle.

`\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}`

Substitute a = 7 and b = 12 into Pythagoras Theorem and solve for c (hypotenuse):

`\implies 7^2+12^2=c^2`

`\implies 49+144=c^2`

`\implies 193=c^2`

`\implies c=√(193)`

`\implies c=13.8924439894...`

Therefore, Amy walks 13.9 blocks (nearest tenth) on her way home.

Part (b)

To calculate the number of blocks Amy walks in one day for her round trip to school and back home, sum the side lengths of the right triangle:

`\implies 7 + 12 + 13.9 = 32.9`

Therefore, Amy walks 32.9 blocks (nearest tenth) in one day for her round trip to school and back home.