Question

Keith left his house for the pool. He rode his bike 3 miles down one road, took a 90-degree turn, and rode another 3 miles down a different road before arriving at the pool. If he had ridden directly to the pool, how much distance would he have saved? Round your answer to the nearest tenth.



(1 point)
Responses

4.2 miles
4.2 miles

1.8 miles
1.8 miles

2.5 miles
2.5 miles

1.2 miles

Answer 1

To find out how much distance Keith would have saved by riding directly to the pool instead of taking the two roads, we can use the Pythagorean theorem.

Keith rode 3 miles down one road and then took a 90-degree turn to ride another 3 miles down a different road. This forms a right triangle where each leg is 3 miles long.

Using the Pythagorean theorem:
\[
c = \sqrt{a^2 + b^2}
\]
where \(a\) and \(b\) are the lengths of the legs of the triangle.

Here, \(a = 3\) and \(b = 3\):
\[
c = \sqrt{3^2 + 3^2} = \sqrt{9 + 9} = \sqrt{18} \approx 4.2426
\]

So the distance Keith would have saved by going directly is the distance he would have traveled (4.2426) subtracted from the total distance he actually traveled (3 + 3 = 6 miles):
\[
\text{Distance saved} = 6 - 4.2426 \approx 1.7574
\]

Rounding it to the nearest tenth gives us:
\[
1.8 \text{ miles}
\]

So, the correct response is:
**1.8 miles**.