The perimeter of the shape below is 11x^2+7x + 1 . Find the length of the missing side. (1 point) Responses 4x^2+5 4 x squared plus 5 −4^x2−2x^2+12 negative 4 x squared minus 2 x squared plus 12 4x^2−8 4 x squared minus 8 −4x^2−2x−7
The perimeter of a shape is the sum of the lengths of all its sides.
Let the lengths of the three known sides be a, b, and c. The perimeter is given by the equation:
P = a + b + c
We are given that the perimeter is:
11x^2 + 7x + 1
Therefore, we have:
11x^2 + 7x + 1 = a + b + c
The lengths of the three known sides are:
a = 4x^2 + 5
b = -4x^2 - 2x^2 + 12 = -6x^2 + 12
c = 4x^2 - 8
Substitute these lengths into the equation for the perimeter:
11x^2 + 7x + 1 = 4x^2 + 5 - 6x^2 + 12 + 4x^2 - 8
Simplify the equation:
11x^2 + 7x + 1 = 2x^2 + 9
Rearrange the equation to solve for x:
9x^2 + 7x - 8 = 0
Factor the quadratic equation:
(9x - 8)(x + 1) = 0
Solve for x:
9x - 8 = 0 or x + 1 = 0
x = 8/9 or x = -1
Since the length of a side cannot be negative, the missing side length cannot be -4x^2 - 2x^2 + 12.
The length of the missing side is:
4x^2 - 8.