Question

In parallelogram ABCD, diagonals AC------- and BD------- intersect at point E, AE = x + 16, and CE=5x

What is AC?
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Answer 1

AC = 40

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