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

2 Answers
Feb 2, 2016

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.

Feb 2, 2016

Answer:

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