In parallelogram ABCD, diagonals AC and BD intersect at point E, AE = x + 16, and CE=5x What is AC?
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AC = 40

Step-by-step explanation:

A quadrilateral is a polygon shape with four sides and four angles. The interior angle of a quadrilateral sums up to 360°.

A parallelogram is a quadrilateral (has four sides and four angles) in which has two pair of opposite sides are parallel to each other. The diagonals of a parallelogram bisect each other.

Given parallelogram ABCD:

Diagonals AC and BD bisect each other at point E. Hence:

AC = AE + CE (line segment addition postulate)

Also:

AE = CE (diagonal BD bisects AC at point E).

Hence; x + 16 = 5x

5x - x = 16

4x = 16

x = 4

AE = x + 16 = 4 + 16 = 20; CE= 5x = 5(4) = 20

AC = AE + CE = 20+ 20 = 40

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step-by-step explanation:

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have