SOLUTION: A triangular space in the shape of a right triangle is to be surrounded on its edge by pebbles. The first side of the space is 6 m. The second side is to be 2m longer than the thi
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Question 1094520: A triangular space in the shape of a right triangle is to be surrounded on its edge by pebbles. The first side of the space is 6 m. The second side is to be 2m longer than the third side. To the nearest tenth, what are the lengths of the second and third sides?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
There are two solutions with the information as given, because the 6m side could be either one of the two legs or the hypotenuse. In either case, since it is a right triangle, the side lengths are related by the Pythagorean Theorem.
We know that the lengths of the second and third sides can be represented by (x+2) and x, respectively. Then...
Case 1: If the 6m side is the longest side, then
This leads to a quadratic equation which has two solutions, both irrational, one of which is negative and can therefore be rejected.
Case 2: If the 6m side is the shortest side, then
This leads to a linear equation with a "nice" solution, so it is very likely the intended answer to the problem.
I leave it to you to finish the solution for the two cases.
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