Question

c is the midpoint of ab. if ac = 3(c + 2), cb = c + 26 find c and the length of ab. if there is no answer, type dne. ab =

Explanation:

Step1: Use the midpoint property

Since \(C\) is the midpoint of \(AB\), \(AC = CB\). So, \(3(c + 2)=c + 26\).

Step2: Solve the equation for \(c\)

Expand \(3(c + 2)\) to get \(3c+6\). The equation becomes \(3c + 6=c + 26\).
Subtract \(c\) from both sides: \(3c - c+6=c - c + 26\), which simplifies to \(2c+6 = 26\).
Subtract \(6\) from both sides: \(2c+6 - 6=26 - 6\), so \(2c=20\).
Divide both sides by \(2\): \(c=\frac{20}{2}=10\).

Step3: Find the length of \(AC\) or \(CB\)

Substitute \(c = 10\) into \(AC = 3(c + 2)\) (or \(CB=c + 26\)).
\(AC=3(10 + 2)=3\times12 = 36\), \(CB=10 + 26=36\).

Step4: Calculate the length of \(AB\)

Since \(AB=AC + CB\) and \(AC = CB = 36\), then \(AB=36+36 = 72\).

Answer:

\(72\)