Question

1. john walks from his house to school in straight lines. he first walks 6 miles to the west, and then walks 8 miles to the north. if john could have taken a helicopter instead of walking, how far would his journey have been?

a. $\frac{4}{3}$
b. 2
c. 10
d. 14
e. 100

Explanation:

Step1: Identify right triangle sides

John's west and north paths form two legs of a right triangle, with lengths $a=6$ miles and $b=8$ miles. The helicopter path is the hypotenuse $c$.

Step2: Apply Pythagorean theorem

Use the formula for the hypotenuse of a right triangle: $c = \sqrt{a^2 + b^2}$
Substitute values: $c = \sqrt{6^2 + 8^2}$

Step3: Calculate the hypotenuse

First compute squares: $6^2=36$, $8^2=64$
Sum: $36+64=100$
Take square root: $c = \sqrt{100}=10$

Answer:

C. 10