Which of the triangles described in the table is a right triangle.
Table
Triangle Q, Side 1=25 Side 2=10 Side 3=15.
Triangle R, Side 1=26 Side 2=20 Side 3=46.
Triangle S, Side 1=25 Side 2=20 Side 3=1,025.
Triangle T, Side 1=25 Side 2=26 Side 3=650.
A. Q
B. R
C. S
D. T
My answer is A
Its not A, use Pythagorean theorem a² + b² = c² plug in those numbers in the formula to see if it is a right triangle.
None of them do
As a matter of fact, the last three don't even form triangles.
the second forms a straight line, notice 20+26 = 46
and the last two fail the basic property that in order to even have a triangle, the sum of any two must be greater than the third side.
for the first one: 15^2 + 10^2 ≠ 25^2
To determine whether a triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Let's apply the Pythagorean theorem to each triangle in the table and calculate the value for each triangle:
For triangle Q with side lengths 25, 10, and 15:
- 25^2 = 10^2 + 15^2
- 625 = 100 + 225
- 625 = 325
- This equation is not true, so triangle Q is not a right triangle.
For triangle R with side lengths 26, 20, and 46:
- 26^2 = 20^2 + 46^2
- 676 = 400 + 2116
- 676 = 2516
- This equation is not true, so triangle R is not a right triangle.
For triangle S with side lengths 25, 20, and 1025:
- 25^2 = 20^2 + 1025^2
- 625 = 400 + 1050625
- 625 = 1051025
- This equation is not true, so triangle S is not a right triangle.
For triangle T with side lengths 25, 26, and 650:
- 25^2 = 26^2 + 650^2
- 625 = 676 + 422500
- 625 = 423176
- This equation is not true, so triangle T is not a right triangle.
Based on these calculations, none of the triangles in the table are right triangles.