The fence around a quadrilateral-shaped pasture is 3a^2+15a+9 long. three sides of the fence have the following lengths: 5a, 10a-2, a^2-7. what is the length of the fourth side of the fence?

The unknown side is 2a^2+18

Step-by-step explanation:

Perimeter is adding all the sides

We have 4 sides so we add all 4 sides.  We will call the 4th side x.  The perimeter is 3a^2+15a+9.  The 3  known sides are 5a, 10a-2, a^2-7.

5a+10a-2 + a^2-7 + x = 3a^2 +15a+9

Combine like terms

15a-9 + a^2 + x = 3a^2 +15a+9

Subtract 15a from each side

15a-15a-9 + a^2 + x = 3a^2 +15a-15a+9

-9+ a^2 + x = 3a^2 +9

Add 9 to each side

-9+9+ a^2 + x = 3a^2 +9+9

a^2 +x = 3a^2 +18

Subtract a^2 from each side

a^2  -a^2+x = 3a^2-a^2 +18

x = 2a^2 +18