Explain if a triangle with the given lengths is a right triangle.
1. 18, 24, 30
2. 7, 24, 25
3. 13, 14, 15
I really do not know how to solve these problems! I have no idea how!!!! Please help!
a^2 + b^2 = c^2
1.
18^2 + 24^2 = C^2
324 + 576 = c^2
900 = c^2
30 = c
The first one is a right triangle.
Do the same thing with the other two problems.
ok thanks but how do you know if "30"
is a right triangle? I thought 90 was a right triangle?
Ahh -- 30 is the length of the hypotenuse (longest side).
http://www.mathsisfun.com/pythagoras.html
thanks
You're welcome.
To determine if a triangle is a right triangle, you can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Now, let's go through each given set of triangle lengths:
1. For the triangle with lengths 18, 24, and 30:
- Square the lengths: 18^2 = 324, 24^2 = 576, 30^2 = 900.
- Check if the sum of the squares of the two shorter sides is equal to the square of the longest side: 324 + 576 = 900.
- Since the two sums are equal, this triangle is a right triangle.
2. For the triangle with lengths 7, 24, and 25:
- Square the lengths: 7^2 = 49, 24^2 = 576, and 25^2 = 625.
- Check if the sum of the squares of the two shorter sides is equal to the square of the longest side: 49 + 576 = 625.
- Again, the two sums are equal, so this triangle is also a right triangle.
3. Lastly, for the triangle with lengths 13, 14, and 15:
- Square the lengths: 13^2 = 169, 14^2 = 196, and 15^2 = 225.
- Calculate the sum of the squares of the two shorter sides: 169 + 196 = 365.
- Since the sum of the squares of the two shorter sides is not equal to the square of the longest side (365 ≠ 225), this triangle is not a right triangle.
Therefore, out of the three triangle sets given, only triangles 1 and 2 are right triangles.