Question

find ad in parallelogram abcd.

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, opposite sides are equal. So \(AD = BC\).
Given \(AD=p + 14\) and \(BC = 9p-26\), we set up the equation \(p+14=9p - 26\).

Step2: Solve the equation for \(p\)

Subtract \(p\) from both sides:
\(14=9p-p - 26\)
\(14 = 8p-26\)
Add \(26\) to both sides:
\(14 + 26=8p\)
\(40=8p\)
Divide both sides by \(8\):
\(p=\frac{40}{8}=5\)

Step3: Find the length of \(AD\)

Substitute \(p = 5\) into the expression for \(AD\) (\(AD=p + 14\)):
\(AD=5+14\)

Answer:

\(19\)