In parallelogram abcd , diagonals ac⎯⎯⎯⎯⎯ and bd⎯⎯⎯⎯⎯ intersect at point e, ae=x2−16 , and ce=6x . what is ac ?

Step-by-step explanation:

We are given a parallelogram ABCD with diagonals AC and BD intersect at point E.

, and CE=6x .

Note: The diagonals of a parallelogram intersects at mid-point.

Therefore, AE = EC.

Plugging expressions for AE and EC, we get

Subtracting 6x from both sides, we get

Factoriong quadratic by product sum rule.

We need to find the factors of -16 that add upto -6.

-16 has factors -8 and +2 that add upto -6.

Therefore, factor of quadratic is (x-8)(x+2)=0

Setting each factor equal to 0 and solve for x.

x-8=0  => x=8

x+2=0  => x=-2.

We can't take x=-2 as it's a negative number.

Therefore, plugging x=8 in EC =6x, we get

EC = 6(8) = 48.

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step-by-step explanation: