Question

Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE=11x−3 and CE=12−4x. Find the length of AC.

Answer 1

AC=16 units

Explanation:

The diagonals of a parallelogram bisect each other. It was given that diagonals AC and BD intersect at point E.

This implies that:
`AE=CE`.

We substitute the expression for x, we get:

`11x-3=12-4x`.

Group similar terms to get:

`11x+4x=12+3`.

`15x=15`.

`x=1`

AC = 2(12-4x)

AC=2(12-4(1))

AC=2(8)

AC=16