Question

the base of a right triangle is (x-5). The height of the triangle is (2x+1). The perimeter of the triangle is (7x+5). Find the area of the triangle and the length of the third side.

Answer 1

Area: (x^2)-(9x/2)-2 3rd side=4x+9

Explanation:

First, let's find the third side. If all of the sums add up to 7x+5, then we can easily subtract the two sides that we do have.

2x+1+x-5=3x-4

Now, you have to ask yourself what added to 3x-4 can be equal to 7x+5.

It's 4x+9 because we combine like terms. That's the third side. Now, we should follow the formula for getting the area of triangle using the side lengths:

(2x+1)(x-5)/2=area of triangle

2x*x=2x^2

2x*-5=-10x

x*1=x

-5*1=-5

Now the total is 2x^2-9x-4 when you continue to combine like terms. Now all we have to do is divide by 2. So, the area is 2x^2-9x-4/2. You can simplify that. Answer is up top.