Question

Given two pieces of steel tubing, one 8 feet long, the other 6 feet long, both joined at one end at an angle of 90 degrees, how long would a third piece need to be to connect the two free ends?

Answer 1

10 feet.

Step-by-step explanation:

The subject of this question is mathematics, specifically geometry and the Pythagorean theorem. The scenario presents a right-angled triangle with an 8-foot tube being one side, a 6-foot tube being the other side, and a third tube being the hypotenuse.

We apply the Pythagorean theorem (a² + b² = c²) where a and b are the lengths of the two legs (sides at a right angle), and c is the length of the hypotenuse. Plugging in our values (8² + 6² = c²), we get 64 + 36 = c², simplifying to 100 = c². The length of the third tube (c), the hypotenuse, is the square root of 100 which equals 10 feet.

Therefore, the third piece of steel tubing would need to be 10 feet long to connect the two free ends.