Question

ac = 143, bc = 8x + 4, and ab = 7x + 4, find bc.

Explanation:

Step1: Use segment - addition postulate

Since $AC = AB + BC$, we substitute the given expressions: $143=(7x + 4)+(8x + 4)$.

Step2: Combine like - terms

$143 = 7x+8x + 4 + 4$, which simplifies to $143=15x + 8$.

Step3: Solve for x

Subtract 8 from both sides: $143−8 = 15x$, so $135 = 15x$. Then divide both sides by 15: $x=\frac{135}{15}=9$.

Step4: Find BC

Substitute $x = 9$ into the expression for $BC$. $BC=8x + 4$, so $BC=8\times9 + 4=72 + 4=76$.

Answer:

76