Questions: If AD=20 and AC=3x+4, find the value of x. Then find AC and DC.

Transcript text: 11.) If $A D=20$ and $A C=3 x+4$, find the value of $x$. Then find $A C$ and $D C$.

Solution

Solution Steps

Step 1: Analyze the given information

The diagram shows that AD and DC are congruent segments, marked with a single hash mark. We are given that AD = 20 and AC = 3x + 4. AC is composed of AD and DC.

Step 2: Set up an equation

Since AD = DC, and AC = AD + DC, we can write AC = 2 * AD. Substituting the given values, we have 3x + 4 = 2 * 20.

Step 3: Solve for x

3x + 4 = 40 3x = 36 x = 12

Step 4: Find AC

AC = 3x + 4 = 3(12) + 4 = 36 + 4 = 40

Step 5: Find DC

DC = AD = 20

Final Answer

x = 12, AC = 40, DC = 20

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