# A right triangle has a perimeter of 12 and sides x, (x + 1), and (x + 2). What is the area of the triangle?

Feb 2, 2016

This is not a right triangle:

Use pythagoras theorem:

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

$a = a \mathrm{dj} a c e n t , b = o p p o s i t e , c = h y p o t e n$$u s e$

The hypotenuse is the longest.

In this triangle the longest side is $x + 2$

So,The the product of the other two sides must equal the hypotenuse.

$\rightarrow x \left(x + 1\right) = x + 2$

$\rightarrow {x}^{2} + x \ne x + 2$

So,This is not a right triangle.

Feb 2, 2016

Area = $6 u n i t {s}^{2}$

#### Explanation:

The perimeter of the triangle is 12 units, so the three sides add up to 12. Therefore $x + \left(x + 1\right) + \left(x + 2\right) = 12$
This simplifies to $3 x + 3 = 12$
which is then $3 x = 9$ so $x = 3$

The formula for the area of a triangle is $\frac{1}{2} \left(b a s e x h e i g h t\right)$, which in this case is $\frac{1}{2}$ (3 x 4) = 6