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

Question

Isaiah Anthony · Accepted Answer

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.

Eva Abramson · Answer

Area = #6units^2# 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

Abigail Allen · Answer

undefined The sides of the right triangle are x, (x + 1), and (x + 2). According to the perimeter formula for a triangle, the sum of all three sides equals the perimeter, which is 12 in this case. So, x + (x + 1) + (x + 2) = 12. Simplifying, we get 3x + 3 = 12, and solving for x, we find x = 3. Now that we know the value of x, we can find the lengths of the sides: x = 3, (x + 1) = 4, and (x + 2) = 5. Using these values, we can calculate the area of the triangle using the formula for the area of a right triangle, which is (base * height) / 2. Here, the base is 3 and the height is 4, so the area is (3 * 4) / 2 = 6 square units. Therefore, the area of the triangle is 6 square units.