Question

points a, b, and c are collinear, and b lies between a and c. if ac = 48, ab = 2x + 2, and bc = 3x + 6, what is bc?

Explanation:

Step1: Use collinear - point property

Since A, B, and C are collinear and B is between A and C, we have $AB + BC=AC$.

Step2: Substitute given expressions

Substitute $AB = 2x + 2$, $BC=3x + 6$, and $AC = 48$ into the equation: $(2x + 2)+(3x + 6)=48$.

Step3: Simplify the left - hand side

Combine like terms: $2x+3x+2 + 6=48$, which gives $5x+8 = 48$.

Step4: Solve for x

Subtract 8 from both sides: $5x=48 - 8=40$. Then divide both sides by 5, so $x=\frac{40}{5}=8$.

Step5: Find the length of BC

Substitute $x = 8$ into the expression for $BC$: $BC=3x + 6=3\times8+6=24 + 6=30$.

Answer:

30