The perimeter is the sum of all sides.
Since we know the values of the individual sides, we can add them all together and create an equation where they equal the value of the perimeter (46).
We're going for the length of each side, so we'll return there once we know what X is.
So we start with:
46 = (x + 3) + (x + 6) + (x^2-3x) + (4x - 3)
Then we combine like terms:
46 = x^2 + (x + x - 3x + 4x) + (3 + 6 - 3)
46 = x^2 + 3x + 6
In order to get this to a solvable form, we'll move the 46 over to the other side by subtracting it from both sides:
0 = x^2 + 3x - 40
Now, to find the value of x, we factor the right side out:
0 = (x + 8) * (x - 5)
In order for this equation to be true, either factor can evaluate out to 0, so...
x = -8 and x = 5
Back to finding the length of each side! Since we know the length of any given side has to be positive, we can toss out the solution where x = -8, because that would cause side 1 to be (-8 + 3) or -5.
So 5 is the correct value for x.
Plug in 5 for all of the sides and evaluate!
Side One: x+3
5 + 3 = 8
Side Two: x+6
5 + 6 = 11
Side Three: x^2-3x
5^2 - 3(5) =
25-3*5=
25-15=
10
Side Four: 4x-3
4*5-3=
20-3=
17
