Question

c is the midpoint of ab.
if ac = c - 40, cb = - 5(c - 4)
find the length of ab. if no answer, type dne.
ab =

Explanation:

Step1: Use the mid - point property

Since \(C\) is the mid - point of \(AB\), \(AC = CB\). So, \(c - 40=-5(c - 4)\).

Step2: Solve the equation for \(c\)

Expand the right - hand side: \(c-40=-5c + 20\).
Add \(5c\) to both sides: \(c + 5c-40=-5c + 5c+ 20\), which gives \(6c-40 = 20\).
Add \(40\) to both sides: \(6c-40 + 40=20 + 40\), so \(6c=60\).
Divide both sides by \(6\): \(c=\frac{60}{6}=10\).

Step3: Find the length of \(AC\)

Substitute \(c = 10\) into \(AC=c - 40\). Then \(AC=10-40=-30\) (length is non - negative, we take the absolute value \(|AC| = 30\)).
Since \(AB=2AC\) (because \(C\) is the mid - point), \(AB = 2\times30\).

Answer:

\(60\)