Question

Jane is training for a triathlon. After swimming a few laps, she leaves the health club and bikes 16 miles south. She then runs 12 miles west. Her trainer bikes from the health club to meet jane at the end of her run. Use the pythagorean theorem to write an equation for the distance janes trainer bikes

Answer 1

Answer:

The equation for the distance Jane's trainer bikes is $x=\sqrt{16^2+12^2}$.

Step-by-step explanation:

We have attached diagram for your reference.

Given:

Distance traveled on bike towards south = 16 miles

Distance she ran towards west = 12 miles

We need to find distance Jane's trainer bikes.

Solution:

Let the distance Jane's trainer bike be 'x'.

Now we will assume it to be right angled triangle.

So by Pythagoras theorem which states that;

"Square of the third side is equal to the sum of square of the other two sides."

framing in equation form we get;

$x^2=16^2+12^2\\\\x=\sqrt{16^2+12^2}$

Hence the equation for the distance Jane's trainer bikes is $x=\sqrt{16^2+12^2}$.

On solving we get;

$x=\sqrt{16^2+12^2}\\\\x= \sqrt{256+144}\\ \\x=\sqrt{400} \\\\x=20\ miles$

Hence Jane's trainer bikes a distance of 20 miles.