If DE = 12, what is AC?
Understand the Problem
The question is asking to find the length of AC, given that DE = 12, and that the shape is a rectangle, with E being the intersection of the diagonals.
Answer
$AC = 24$
Answer for screen readers
$AC = 24$
Steps to Solve
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Properties of Rectangles In a rectangle, the diagonals are equal in length and bisect each other. This means they cut each other in half.
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Relating DE and AC Since E is the intersection of the diagonals AC and BD, and the diagonals bisect each other, then $DE = \frac{1}{2}BD$. Also, $AC = BD$ because the diagonals of a rectangle are equal.
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Calculate BD Given that $DE = 12$, we can calculate the length of $BD$. $BD = 2 \cdot DE = 2 \cdot 12 = 24$
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Calculate AC Since $AC = BD$, we have $AC = 24$
$AC = 24$
More Information
The diagonals of a rectangle are equal in length and bisect each other. This property is key to solving this problem.
Tips
A common mistake is to assume that $DE = AC$, confusing the half-length of the diagonal with the full length of the other one. Another mistake is thinking diagonals are not equal in rectangle.
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