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In the figure below, BE=5,DE=x+2 and AC=3x What is the length of overline (AC) 3 6 10 12

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In the figure below, BE=5,DE=x+2 and AC=3x
What is the length of overline (AC)
3
6
10
12

In the figure below, BE=5,DE=x+2 and AC=3x What is the length of overline (AC) 3 6 10 12

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UnityElite · Tutor for 8 years

Answer

To find the length of \(\overline{AC}\), we need to use the information given in the picture details and the question.Step 1: Identify the known lengths.- \(AD = x + 2\)- \(AE = 3x\)- \(BE = 5\)- \(DE = x + 2\)Step 2: Use the properties of the triangles.Since \(\triangle ABD\) and \(\triangle AED\) share the same vertex A and the side AD, we can use the fact that \(AE = AD + DE\).Step 3: Set up the equation.According to the information given, we have:\(AE = AD + DE\)\(3x = (x + 2) + (x + 2)\)Step 4: Simplify the equation.\(3x = 2x + 4\)Step 5: Solve for x.Subtract \(2x\) from both sides of the equation:\(3x - 2x = 4\)\(x = 4\)Step 6: Find the length of \(\overline{AC}\).Since \(AC = AE\) and \(AE = 3x\), we substitute the value of x into the equation:\(AC = 3(4)\)\(AC = 12\)Answer: The length of \(\overline{AC}\) is 12.
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