Answer:
3
Step-by-step explanation:
If it's a right triangle, the Pythagorean theorem applies. Remember that is
[tex]a^{2} + b^{2} = c^{2}[/tex]
The longest side (c) will be x+2, and the other two sides are a and b.
[tex]x^{2} + (x+1)^{2} = (x+2)^{2}[/tex]
Now we have to solve this all out. :(
[tex]x^{2} + x^{2} + 2x + 1 = x^2 + 4x + 4[/tex]
Combine like terms.
[tex]2x^{2} + 2x + 1 = x^2 + 4x + 4[/tex]
Move everything to one side, combining like terms.
[tex]x^{2} - 2x -3 = 0[/tex]
Now factor.
(x-3)(x+1) = 0
x = 3 or -1.
Clearly a side can't be -1 units, so the answer is 3.
You also can do this much faster if you remember the Pythagorean triple 3, 4, 5.
Answer:
Step-by-step explanation:
If it is a right triangle , then Pythagorean Theorem will apply
x+2 will be the hypotenuse (longest)
x^2 + (x+1)^2 = (x+2)^2
x^2 + x^2 +2x+1 = x^2 + 4x+4
x^2 -2x-3 = 0 Quadratic formula shows x =3 cm
