Question

The perimeter of the shape below is 21x2−5x + 4
. Find the length of the missing side.
2x-3
7x^2+3x+2
2x-3


(1 point)
Responses

4x2+5
4 x squared plus 5

−14x2+12x−8
negative 14 x squared plus 12 x minus 8

14x2−12x+8
14 x squared minus 12 x plus 8

4x2−8

Answer 1

To find the length of the missing side given the perimeter of the shape and the lengths of the other sides, we need to first express the perimeter in terms of the lengths of all the sides.

Let's denote the sides of the shape as follows:
- Side 1: \(2x - 3\)
- Side 2: \(7x^2 + 3x + 2\)
- Side 3: \(2x - 3\)
- Side 4: \(L\) (the missing side)

The perimeter \(P\) is given by:
\[
P = \text{Side 1} + \text{Side 2} + \text{Side 3} + \text{Side 4}
\]

Substituting in the values we have:
\[
21x^2 - 5x + 4 = (2x - 3) + (7x^2 + 3x + 2) + (2x - 3) + L
\]

Combining the known sides (Side 1, Side 2, Side 3):
\[
= (2x - 3) + (2x - 3) + (7x^2 + 3x + 2)
= (2x + 2x + 3x) + (7x^2) + (-3 - 3 + 2)
\]
\[
= 7x^2 + 7x - 4
\]

Now, we set the equation for the perimeter:
\[
21x^2 - 5x + 4 = (7x^2 + 7x - 4) + L
\]

To find \(L\), we rearrange the equation:
\[
L = (21x^2 - 5x + 4) - (7x^2 + 7x - 4)
\]

We can simplify further by distributing the negative sign:
\[
L = 21x^2 - 5x + 4 - 7x^2 - 7x + 4
\]

Combining like terms:
\[
= (21x^2 - 7x^2) + (-5x - 7x) + (4 + 4)
\]
\[
= 14x^2 - 12x + 8
\]

Thus, the length of the missing side is:
\[
\boxed{14x^2 - 12x + 8}
\]