Two poles of heights 7 m and 12m stand on a plane ground. If the distance between the feet of the poles be 12 m, then find the distance between their tops.

Answer

To find the distance between the tops of two poles of heights 7 m and 12 m that are 12 m apart at their bases, we can use the Pythagorean theorem. Here’s a step-by-step solution:

### Step 1: Identify the heights of the poles
Let the height of the first pole (A) be 12 m and the height of the second pole (B) be 7 m.

### Step 2: Calculate the vertical distance between the tops of the poles
The vertical distance between the tops of the two poles can be calculated as:
\[ \text{Height of pole A} - \text{Height of pole B} = 12 \, \text{m} - 7 \, \text{m} = 5 \, \text{m} \]

### Step 3: Identify the horizontal distance between the poles
The horizontal distance between the feet of the poles is given as 12 m.

### Step 4: Use the Pythagorean theorem
Now, we can form a right triangle where:
- One leg (vertical distance) = 5 m
- The other leg (horizontal distance) = 12 m
- The hypotenuse (distance between the tops of the poles) = EC

According to the Pythagorean theorem:
\[ EC^2 = ED^2 + DC^2 \]
Where:
- \( ED = 5 \, \text{m} \) (the vertical distance)
- \( DC = 12 \, \text{m} \) (the horizontal distance)

Substituting the values:
\[ EC^2 = 5^2 + 12^2 \]
\[ EC^2 = 25 + 144 \]
\[ EC^2 = 169 \]

### Step 5: Calculate the distance EC
Now, take the square root of both sides:
\[ EC = \sqrt{169} = 13 \, \text{m} \]

### Final Answer
The distance between the tops of the two poles is **13 m**.

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