Question

1. if ( ab = 4x + 21 ), ( bc = 6x + 15 ), and ( cd = 8x + 1 ), what is ( cd )?

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, \(AB = CD\) and \(AD=BC\). But from the markings (equal - length marks), we assume \(AB = CD\) (since in a parallelogram, opposite sides are equal). So we set up the equation \(4x + 21=8x + 1\).

Step2: Solve the equation for \(x\)

Subtract \(4x\) from both sides: \(21=4x + 1\).
Subtract \(1\) from both sides: \(20 = 4x\).
Divide both sides by \(4\): \(x = 5\).

Step3: Find the length of \(CD\)

Substitute \(x = 5\) into the expression for \(CD\): \(CD=8x+1\).
\(CD=8\times5 + 1=40 + 1=25\).

Answer:

\(25\)