SOLUTION: The perimeter of a triangle is 85 inches. The sides are: 2x, 2x+5, and X squared + 3 Find the legths of the sides. I though of putting them all together and then factoring, bu

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The perimeter of a triangle is 85 inches. The sides are: 2x, 2x+5, and X squared + 3 Find the legths of the sides. I though of putting them all together and then factoring, bu      Log On


   

Question 76887This question is from textbook Prealgebra and Introductory Algebra
: The perimeter of a triangle is 85 inches. The sides are: 2x, 2x+5, and X squared + 3 Find the legths of the sides.
I though of putting them all together and then factoring, but it wasn't working out. If someone could help me I would really appreciate it.
Thank you very much for your time. This question is from textbook Prealgebra and Introductory Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If we add all of the sides we get the perimeter, so
%282x%29%2B%282x%2B5%29%2B%28x%5E2%2B3%29=85
x%5E2%2B4x%2B8-85=0 Combine like terms and get all terms to one side
x%5E2%2B4x-77=0
Now we can factor the left side
Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor 1%2Ax%5E2%2B4%2Ax%2B-77, first we need to ask ourselves: What two numbers multiply to -77 and add to 4? Lets find out by listing all of the possible factors of -77


Factors:

1,7,11,77,

-1,-7,-11,-77,List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to -77.

(-1)*(77)=-77

(-7)*(11)=-77

Now which of these pairs add to 4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 4

||||
First Number|Second Number|Sum
1|-77|1+(-77)=-76
7|-11|7+(-11)=-4
-1|77|(-1)+77=76
-7|11|(-7)+11=4
We can see from the table that -7 and 11 add to 4.So the two numbers that multiply to -77 and add to 4 are: -7 and 11 Now we substitute these numbers into a and b of the general equation of a product of linear factors which is: %28x%2Ba%29%28x%2Bb%29substitute a=-7 and b=11 So the equation becomes: (x-7)(x+11) Notice that if we foil (x-7)(x+11) we get the quadratic 1%2Ax%5E2%2B4%2Ax%2B-77 again


So the quadratic x%5E2%2B4x-77=0 factors to %28x-7%29%28x%2B11%29=0
Now set each term equal to zero
x-7=0
x=7
x%2B11=0
x=-11 This answer doesn't make any sense (a negative length doesn't work)
So our answer is 7


Check:
%282%287%29%29%2B%282%287%29%2B5%29%2B%28%287%29%5E2%2B3%29=85
%2814%29%2B%2814%2B5%29%2B%2849%2B3%29=85
%2814%29%2B%2819%29%2B%2852%29=85
85=85 works