Question

1. gn = 6x + 1

ge = 11x + 5
find ge
(there is a diagram of a parallelogram (or rectangle/quadrilateral) with vertices g, f, e, h and diagonals intersecting at n)

Explanation:

Step1: Recall properties of parallelograms

In a parallelogram, the diagonals bisect each other. So, \( GN = NE \) and \( GE = GN + NE = 2GN \). Also, we know \( GE = 11x + 5 \) and \( GN = 6x + 1 \). Since \( GE = 2GN \), we can set up the equation:
\( 11x + 5 = 2(6x + 1) \)

Step2: Solve for x

Expand the right side: \( 11x + 5 = 12x + 2 \)
Subtract \( 11x \) from both sides: \( 5 = x + 2 \)
Subtract 2 from both sides: \( x = 3 \)

Step3: Find GE

Substitute \( x = 3 \) into the expression for \( GE \): \( GE = 11(3) + 5 = 33 + 5 = 38 \)

Answer:

\( GE = 38 \)