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3 years ago

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

Mathematics

1 answer:

Oxana [17]3 years ago

8 0

Answer:

AC=16 units

Step-by-step 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

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murzikaleks [220]

We first approach this problem by illustrating the situation. Refer to the diagram attached.

From the diagram, we can clearly see that we need to simply solve for the length marked x in order to find the distance between the foot of the ladder to the base of the wall.

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