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

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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)   (Show Source): You can put this solution on YOUR website!
If we add all of the sides we get the perimeter, so

Combine like terms and get all terms to one side

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 , 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: substitute 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 again


So the quadratic factors to
Now set each term equal to zero



This answer doesn't make any sense (a negative length doesn't work)
So our answer is 7


Check:



works

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