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14 days ago

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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

1 answer:

PIT_PIT [12.4K]14 days ago

7 0

Answer:

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

Detailed explanation:

A diagram has been included for clarity.

Known values:

Distance biked to the south = 16 miles

Distance ran west = 12 miles

We need to determine the distance covered by Jane's trainer.

Solution:

Let the biking distance be represented by 'x'.

We will assume it forms a right-angled triangle.

According to the Pythagorean theorem, it states that;

"The square of the hypotenuse is equal to the sum of the squares of the other two sides."

When set in equation form, this gives us;

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

Thus, the equation representing the distance biked by Jane's trainer is $x=\sqrt{16^2+12^2}$ .

Upon solving, we find;

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

Consequently, Jane's trainer covers a distance of 20 miles.

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