Question

From his home, glenn travels 3 miles east, 4 miles north, 6 miles east, and then 8 miles north before finally reaching his destination. Assuming his entire trip occurred on a single flat plane, how many miles in a direct line is glenn's home from his destination?

Answer 1

In order to solve this, you need a diagram.

From this diagram, you can set up an expression.
Let's say the total distance is represented by the variable T.


`T=x+y`

To solve for x and y, you need to do the Pythagorean Theorem.


`x^2=3^2+4^2 \\ x^2=9+16 \\ x^2=25 \\ √( x^2) = √(25) \\ x=5 \\ \\ y^2=6^2+8^2 \\ y^2=36+64 \\ y^2=100 \\ √( y^2) = √(100) \\ y=10`

Now plug these values back into the expression and you will have your final answer.


`T=(5)+(10) \\ T=15 \\ \\ 15_(miles)`