Question

Keith left his house, rode his bike 3 miles along one road, took a 90 degree turn and rode 3 miles to the local swimming pool. If he had ridden directly to the pool, how much distance would he have saved? Round the answer to the nearest tenth of a mile.

Answer 1

1.8 miles

Explanation:

Let's figure out the total distance he has actually ridden: 3 + 3 = 6 miles.

Now, let's draw this out (see attachment). Notice that if Keith rode his bike directly to the pool, we'd have a right triangle with legs 3 and 3 and with the hypotenuse as the direct path.

Use the Pythagorean Theorem to figure out the hypotenuse length:

c = √(3² + 3²) = √(9 + 9) = √18 = 3√2 ≈ 4.2 miles

Subtract this from 6:

6 - 4.2 = 1.8

The answer is 1.8 miles.

Answer 2

1.8 miles

Explanation:

For this case we can model the problem as a rectangle triangle.

We know:

Length of the sides of the triangle

We want to know:

Length of the hypotenuse

Using the Pythagorean theorem we have:

`d=\sqrt{3^(2) +3^(2) }\\d = √(2(3^2)) \\d = 3√(2) \\d = 4.2 miles`

Then, the distance that he would have saved if he travels directly is:

`3 + 3 - 4.2 = 1.8 miles`

Answer:

he would have saved:

1.8 miles