Question

1. if ad = 3x + 18, ab = 5x + 10, and bc = 12x + 2, what is bc?

options: 30, 15.7, 50, 19.5

Explanation:

Step1: Identify congruent sides

From the diagram: $AD = AB$, $BC = DC$

Step2: Set up equation for $x$

Substitute given expressions:
$3x + 18 = 5x + 10$

Step3: Solve for $x$

Rearrange to isolate $x$:
$18 - 10 = 5x - 3x$
$8 = 2x$
$x = \frac{8}{2} = 4$

Step4: Calculate length of $BC$

Substitute $x=4$ into $BC = 12x + 2$:
$BC = 12(4) + 2 = 48 + 2 = 50$

Answer:

50