What is the equation to figure out this problem?

Question

Two cars start off at the same point on a straight highway facing opposite directions. Each car drives for 6 miles, takes a left turn, and drives for 8 miles. How far apart are the two cars?

Answer 1

2*Square Root of (6^2+8^2)

or if p miles first, then take a 90 degree turn and q miles

2* Square Root of (p^2+q^2)

Answer 2

20 miles is the answer.

You use the Pythagorean theorem to solve.

squareroot(6^2 + 8^2) = 10 miles from the starting point, and each car is that far away, so the total is 20 miles.

Also... I did it in my head. There is one right-triangle type called the "3-4-5" triangle that is easy to memorize. If the 2 sides are ratio 3 and 4, then the hypoteneuse is 5. In this case 6 and 8 are ratio 3 and 4 (times 2), so the hypoteneuse is 5*2.
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Answer 3

20 miles apart

When you draw out where the cars go and draw in the line to connect them (how far apart they are), it forms two triangles. You can go the long way and do a^2 + b^2 = c^2 to get the hypotenuse (sp?) for the two triangles. Or, if you recognize that these are 3-4-5 triangles doubled (6-8-10), then you know the hypotenuse for each triangle is 10 miles. Add them together and you get the 20 miles

Answer 4

If a segment connecting the end points is drawn, the resultant pattern will form two right triangles, with the cars at opposite ends of the respective hypothenuses. Calculate length of the hypothnenuse, which will be the same in each case, and add.

These are 3-4-5 triangles (values doubled). Distance = 10 mi. each so 20 in total

Answer 5

20 miles apart

You use the Pythagorean theorem to solve. Each car is 10 miles from the starting point, then you double it, because each car went the same distance, only in opposite directions.