Question

The lengths of the sides of a triangle are x cm, (x+1) cm and (x+2) cm . Determine x so that this triangle is a right -angled triangle.

Answer 1

Answer:

3

Step-by-step explanation:

If it's a right triangle, the Pythagorean theorem applies. Remember that is

$a^{2} + b^{2} = c^{2}$

The longest side (c) will be x+2, and the other two sides are a and b.

$x^{2} + (x+1)^{2} = (x+2)^{2}$

Now we have to solve this all out. :(

$x^{2} + x^{2} + 2x + 1 = x^2 + 4x + 4$

Combine like terms.

$2x^{2} + 2x + 1 = x^2 + 4x + 4$

Move everything to one side, combining like terms.

$x^{2} - 2x -3 = 0$

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 2

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