SOLUTION: A triangle has a perimeter of 18cm. Find the length of each side. The sides are: x+2 x^2-x 2x+1

Algebra ->  Triangles -> SOLUTION: A triangle has a perimeter of 18cm. Find the length of each side. The sides are: x+2 x^2-x 2x+1      Log On


   

Question 849610: A triangle has a perimeter of 18cm. Find the length of each side.
The sides are:
x+2
x^2-x
2x+1
Found 2 solutions by pmesler, ewatrrr:
Answer by pmesler(52) About Me  (Show Source):
You can put this solution on YOUR website!
First, you need to know that the perimeter of a triangle is
P = a + b + c.

Since we already know the perimeter, we simply plug that into the formula along with the three sides given and we simply solve for x.
18 = (x^2-x) + (2x+1) + (x+2).
Combine like terms and simplify.
18 = x^2-x + 3x + 3
18 = x^2+2x + 3. Since we have a second degree equation, this is quadratic. Therefore we will need to make the entire equation equal to zero to find the values of x, or the roots of the equation. Do this by subtracting 18 from both sides.
x^2+2x-15 = 0. Now use the quadratic formula to find x:

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-15+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%282%29%5E2-4%2A1%2A-15=64.

Discriminant d=64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+64+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+64+%29%29%2F2%5C1+=+3
x%5B2%5D+=+%28-%282%29-sqrt%28+64+%29%29%2F2%5C1+=+-5

Quadratic expression 1x%5E2%2B2x%2B-15 can be factored:
1x%5E2%2B2x%2B-15+=+1%28x-3%29%2A%28x--5%29
Again, the answer is: 3, -5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-15+%29


From this you can see that x is either -5 or 3.
Let's plug in each value of x into the original equation to see which answer we can disregard and which one we should accept as the correct value for x.
18 = (x^2-x) + (2x+1) + (x+2)

18 = (-5^2-5) + (2(-5)+1) + (-5+2)
18 = 20 -9 + -3
18 = 11-3
18 = 8. This is obviously false so we can disregard -5 since it is an extraneous root. Now let's try the equation when x = 3.

18 = (3^2-3) + (2(3)+1) + (3+2)
18 = 6 + 7 + 5
18 = 18 This checks out. Therefore the lengths of the different sides of the triangle are 5,6,and 7.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

x+2 + x^2-x + 2x+1 = 18cm

 x^2 + 2x -15 = 0   

(x+5)(x-3) = 0   (Tossing out x = -5 that results in negative lengths)

     x = 3

lengths of each side:   5cm, 6cm, 7cm

CHECKING our answer***

5cm + 6cm + 7cm = 18cm

Wish You the Best in your Studies.