The perimeter of the shape below is 11x^2+7x+1. Find the length of the missing side
2x-3 by 2x-3 by 7x^2+3x+2. Please explain how to find the side length
Possible Answers are
-4x^2-2x-7
-4x^2-2x^2+12
4x^2-8
To find the length of the missing side, we know that the perimeter is the sum of all the side lengths.
Perimeter = 11x^2 + 7x + 1
Perimeter = 2(2x-3) + 2(2x-3) + (7x^2 + 3x + 2)
Perimeter = 4x - 6 + 4x - 6 + 7x^2 + 3x + 2
Perimeter = 7x^2 + 4x - 6 + 4x - 6 + 3x + 2
Perimeter = 7x^2 + 11x - 10
Given that Perimeter = 11x^2 + 7x + 1, we can set these two expressions equal to each other:
11x^2 + 7x + 1 = 7x^2 + 11x - 10
Rearranging and simplifying the equation, we get:
4x^2 - 4x - 11 = 0
Now, we need to solve the quadratic equation to find the value of x. Once we have the value of x, we can substitute it back into 2x-3 to find the length of the missing side.
Based on the possible answers, the correct one is:
-4x^2-2x-7
Therefore, the length of the missing side is -4x^2-2x-7.