Which of the triangles described in the table is a right triangle?
side 1 side 2 side3
q 25 20 15
r 26 20 46
s 25 20 1025
t 25 26 650
I think that it is R
The answer is S.
A right angle triangle follows Theorem Phytagoras rule. The sum of squares of 2 sides = length of the 3rd side
For S, 25^2 + 20^2 = 1025
Not quite. sum of squares is the square of the 3ed side.
We all know of the 3-4-5 triangle.
Scale that up by a factor of 5 and you get a 15-20-25 triangle. (q)
(s) and (t) are just way off. We know that for any triangle, each side is less than the sum of the other two.
Square of the 3rd side is the hypothenuse.
If we square root 1025, we'll get 5sqrt(41).
5sqrt(41) - 20^2 = 625 = 25^2
To determine whether a triangle is a right triangle, we can use the Pythagorean theorem, which states that for 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 lengths of the other two sides.
Let's apply this theorem to each of the triangles described in the table:
For triangle q:
- Side 1: 25
- Side 2: 20
- Side 3: 15
To check if it's a right triangle, we can calculate the squares of each side and see if they satisfy the Pythagorean theorem:
25^2 = 625
20^2 = 400
15^2 = 225
Based on the theorem, if it was a right triangle, the square of the hypotenuse (625) would be equal to the sum of the squares of the other two sides (400 + 225 = 625). In this case, it matches, so triangle q is a right triangle.
For triangle r:
- Side 1: 26
- Side 2: 20
- Side 3: 46
Let's calculate the squares:
26^2 = 676
20^2 = 400
46^2 = 2116
Again, checking if the squares satisfy the Pythagorean theorem:
676 = 400 + 2116
676 ≠ 2516, so triangle r is not a right triangle.
For triangle s:
- Side 1: 25
- Side 2: 20
- Side 3: 1025
Calculating the squares:
25^2 = 625
20^2 = 400
1025^2 = 1050625
Applying the Pythagorean theorem:
625 + 400 ≠ 1050625, so triangle s is not a right triangle.
For triangle t:
- Side 1: 25
- Side 2: 26
- Side 3: 650
Squaring the sides:
25^2 = 625
26^2 = 676
650^2 = 422500
Checking the squares against the Pythagorean theorem:
625 + 676 = 1301 ≠ 422500, so triangle t is not a right triangle.
Therefore, the right triangle out of the given options is triangle q.