Question

1. the total length of the fence around (perimeter) a quadrilateral-shaped garden shown is $3a^2 + 15a + 9$. what expression represents the missing fence length?

$5a$
$10a - 2$
$a^2 - 7$

Explanation:

Step1: Sum known side lengths

$(5a) + (10a - 2) + (a^2 - 7)$
$= a^2 + (5a + 10a) + (-2 - 7)$
$= a^2 + 15a - 9$

Step2: Subtract sum from perimeter

$(3a^2 + 15a + 9) - (a^2 + 15a - 9)$
$= 3a^2 + 15a + 9 - a^2 - 15a + 9$
$= (3a^2 - a^2) + (15a - 15a) + (9 + 9)$

Answer:

$2a^2 + 18$