Explain and Prove that the sides of the triangles below are a right triangle. 1.) 5, 10,12

2.) 6,5,3

3.) 3, 4, 5

4.) 6, 8,10

*Pls explain all ill give you brainliest or w.e its called*

3.) 3, 4, 5
&
4.) 6, 8, 10
Those two are right triangles because when you add the squares of the first two it should give you the square root of the third number

a^2 + b^2 = c^2

So
3^2 + 4^2 = 5^2
9 + 16 = 25
25 = 25

6^2 + 8^2 = 10^2
36 + 64 = 100
100 = 100

Therefore they are right triangles

But 1 & 2 aren’t right triangles because when you add the squares of the first two number, it doesn’t equal to the square root of the third number.

Hope this helps!!

We start from the third equation:

4z = 16     divide both sides by 4

z = 4

Put the value of z to the second equation:

y + 4 = 5      subtract 4 from both sides

y = 1

Put the values of y and z to the first equation:

3x + 2(1) - 4 = 4

3x + 2 - 4 = 4

3x - 2 = 4      add 2 to both sides

3x = 6      divide both sides by 3

x = 2
x = 2, y = 1, z = 4 → (2, 1, 4)