Question

the perimeter of the pentagon below is 57 units. find the length of side $overline{bc}$. write your answer without variables. the side lengths of the pentagon: $de=2z$, $cd=10$, $bc=z+3$, $ab=3z-2$, $ae=10$

Explanation:

Step1: Sum all side lengths

$2z + 10 + (z+3) + (3z-2) + 10$

Step2: Simplify the perimeter equation

$2z + 10 + z + 3 + 3z - 2 + 10 = 57$
$6z + 21 = 57$

Step3: Solve for z

$6z = 57 - 21$
$6z = 36$
$z = \frac{36}{6} = 6$

Step4: Calculate length of $\overline{BC}$

$BC = z + 3 = 6 + 3$

Answer:

9