Question

NRTW is a parallelogram whose diagonals intersect at point B. Some of the measurements are shown.

NW 6x 10.5
BW= 6x- 7.7
TB = 2x + 11.6
TW = 6x + 16
WR = 221
Write an equation that can be used to determine the value of x._
A. 2(6x-7.7)-221
B. 6x +16=221
C. 6x-7.7-6x - 10.5
D. 6x +16=2x +11.6

Answer 1

The correct equation to determine the value of x in parallelogram NRTW is 6x + 16 = 221, corresponding to option B.

Let's use the properties of a parallelogram to write an equation involving the given measurements.

In a parallelogram, opposite sides are equal. Therefore, we can set up an equation using the measurements provided: NW + TB = BW + TW

Substitute the given expressions: 6x + 10.5 + (2x + 11.6) = (6x - 7.7) + (6x + 16)

Now, simplify and solve for x: 8x + 22.1 = 12x + 8.3

Subtract 8x from both sides: 22.1 = 4x + 8.3

Subtract 8.3 from both sides: 13.8 = 4x

Divide by 4: x = 3.45

Now, let's check which answer choice corresponds to the correct equation: 6x + 16 = 221

This matches with option: B. 6x + 16 = 221