Question

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

Answer 1

This is not a right triangle:

Use pythagoras theorem:

`a^2+b^2=c^2`

`a=adjacent,b=opposite,c=hypoten` `use`

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.

`rarrx(x+1)=x+2`

`rarrx^2+x!=x+2`

So,This is not a right triangle.

Answer 2

Area = `6units^2`

Explanation:

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

The formula for the area of a triangle is `1/2(base x height)`, which in this case is `1/2` (3 x 4) = 6