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

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

Answer 2

3

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.