Question

parallelograms
figure cdef is a parallelogram.
which equations are correct? choose three correct answers.
( n = 10 )
( cd = 30 )
( cf = 59 )
( fe = 42 )
( n = 7 )

Explanation:

Step1: Use the property of parallelogram (opposite sides are equal)

In parallelogram \(CDEF\), \(CF = DE\) and \(CD=FE\). So, \(6n - 1=5n + 9\).

Step2: Solve the equation \(6n - 1=5n + 9\)

Subtract \(5n\) from both sides: \(6n-5n-1 = 5n - 5n+9\), which gives \(n-1=9\). Then add \(1\) to both sides: \(n=9 + 1=10\).

Step3: Calculate the lengths of the sides

If \(n = 10\), then \(CD=4n + 2=4\times10+2=42\), \(CF=6n-1=6\times10 - 1=59\), \(FE = CD = 42\) (since \(CD = FE\) in a parallelogram).

Answer:

\(n = 10\), \(CF = 59\), \(FE = 42\)