In parallelogram ABCD , diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E, AE=x2−16 , and CE=6x . What is AC ? Enter your answe

Question

4 years ago

7

r in the box.

1 answer:

7nadin3 [17] · Answer 1 · 2022-01-14T11:05:32+03:00

Answer:

<h3>AC = 96 units.</h3>

Step-by-step explanation:

Given ABCD is a parallelogram.

And diagonals AC and BD intersects at point E.

<em>Note: Diagonals of a parallelogram intersects at mid-point.</em>

E is the mid point of diagonal AC

Therefore,

AE = CE.

Plugging expression for AE and CE, we get

$x^2-16 =6x.$

Subtracting 6x from both sides, we get

$x^2-16-6x = 6x-6x$

$x^2 -6x -16 =0$

Factoring quadratic

(x+2)(x-8) =0.

x+2 =0 => x=-2.

x-8=0 => x=8.

We can't take the length by a negative number. Therefore, x=8.

Now, plugging x= 8 in CE =6x, we get

CE = 6(8) = 48.

We need to find the length of AC.

<em>AC would be two times of CE.</em>

Therefore, AC = 2 × 48 = 96.