Answer:
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
