MTH 157
posted by Rayna on .
I need help on these two questions.
1. Describe what happens to the three points of concurrency that determine the Euller lines when the triangle is (a) isosceles, (b) equilateral
2. Which of the following triples of numbers can be the sides of a right triangle? Explain why. (a)square root 3, square root 4, square root 7, (b) 0.3, 0.4, 0.5, (c) 10, 24, 26, (d) 2, 3, 4
I have tried to look up these but don't get how to work them or what I am looking for.

1. When the triangle is isosceles, the three points are collinear, i.e. a straight line passes through the three points.
In the case of an equilateral triangle, all three points coincide at the centroid of the triangle.
See also:
http://en.wikipedia.org/wiki/Euler_line
2. Use Pythagoras theorem, which states that the square of the hypothenuse (the longest side) of a righttriangle is equal to the sum of the squares of the remaining sides.
For example,
3²+4²
=9+16
=25
5²
=25
Therefore the triangle 3,4,5 is a righttriangle. 
Thank you for the help. When you gave the example of question 2 is that I need to put for explaining my answer?

Yes, explanations similar to the example would suffice.
However, you need to check in a similar way each of the triplets given in the question.
You will notice that there is one of the four triplets is not Pythagorean.