Question

points q and r are midpoints of the sides of triangle abc. what is aq? 10 units 14 units 20 units 32 units

Explanation:

Step1: Use the mid - segment theorem

The mid - segment theorem states that the length of the mid - segment (\(QR\)) is half the length of the third side (\(BC\)). So, \(2(2p + 3)=6p - 4\).

Step2: Solve the equation for \(p\)

Expand the left - hand side: \(4p+6 = 6p - 4\).
Subtract \(4p\) from both sides: \(6=2p - 4\).
Add \(4\) to both sides: \(10 = 2p\).
Divide both sides by \(2\): \(p = 5\).

Step3: Find the length of \(AQ\)

Since \(AQ = 4p\), substitute \(p = 5\) into the expression. Then \(AQ=4\times5\).

Answer:

\(20\) units