In rectangle ABCD, diagonals AC and BD intersect at E. If AE=3x-28 and DE=.5x+12, find the length of AC.

Given:

In rectangle ABCD, diagonals AC and BD intersect at E, AE=3x-28 and DE=.5x+12.

To find:

The length of AC.

Solution:

We know that, diagonals of a rectangle are equal and they bisect each other.

In rectangle ABCD, diagonals AC and BD intersect at E, so

         ...(i)

Taking , we get

Divide both sides by 2.5.

Now,

Using segment addition property,

        [Using (i)]

Therefore, the length of AC is 40 units.

24+x=y

step-by-step explanation: