A man walked 20m to cross a rectangular field diagonally if the length of the field is 12m the breadth of the field is:

Options

A. 4m
B. 16m
C. 12m
D. 14m

Answer

To solve the problem of finding the breadth of a rectangular field when a man walks diagonally across it, we can use the Pythagorean theorem. Here’s the step-by-step solution:

### Step 1: Understand the Problem
We have a rectangular field where:
- The length (l) = 12 m
- The diagonal distance walked (hypotenuse, h) = 20 m
- The breadth (b) is what we need to find.

### Step 2: Set Up the Pythagorean Theorem
According to the Pythagorean theorem, in a right triangle:
\[ h^2 = l^2 + b^2 \]
Where:
- \( h \) is the hypotenuse (diagonal),
- \( l \) is the length,
- \( b \) is the breadth.

### Step 3: Substitute the Known Values
Substituting the known values into the equation:
\[ 20^2 = 12^2 + b^2 \]

### Step 4: Calculate the Squares
Now calculate the squares:
\[ 400 = 144 + b^2 \]

### Step 5: Rearrange the Equation
To find \( b^2 \), rearrange the equation:
\[ b^2 = 400 - 144 \]

### Step 6: Perform the Subtraction
Now perform the subtraction:
\[ b^2 = 256 \]

### Step 7: Take the Square Root
To find \( b \), take the square root of both sides:
\[ b = \sqrt{256} \]
\[ b = 16 \]

### Conclusion
The breadth of the rectangular field is **16 meters**.

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