The length of a rectangle is 24 cm.If the length of diagonal is 26 cm, then what will be the breadth of the rectangle?

Options

A. 12 cm
B. 14 cm
C. 15 cm
D. 10 cm

Answer

To find the breadth of the rectangle given its length and the length of the diagonal, we can use the Pythagorean theorem. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Length of the rectangle (l) = 24 cm
- Length of the diagonal (d) = 26 cm
- Let the breadth of the rectangle be (b).

### Step 2: Apply the Pythagorean theorem
In a rectangle, the diagonal forms a right triangle with the length and breadth. According to the Pythagorean theorem:
\[ d^2 = l^2 + b^2 \]

### Step 3: Substitute the known values into the equation
Substituting the values we have:
\[ 26^2 = 24^2 + b^2 \]

### Step 4: Calculate the squares
Calculate \( 26^2 \) and \( 24^2 \):
- \( 26^2 = 676 \)
- \( 24^2 = 576 \)

### Step 5: Set up the equation
Now substitute these values back into the equation:
\[ 676 = 576 + b^2 \]

### Step 6: Rearrange the equation to solve for b^2
To find \( b^2 \), rearrange the equation:
\[ b^2 = 676 - 576 \]

### Step 7: Perform the subtraction
Calculate \( 676 - 576 \):
\[ b^2 = 100 \]

### Step 8: Take the square root to find b
Now take the square root of both sides to find \( b \):
\[ b = \sqrt{100} \]
\[ b = 10 \, \text{cm} \]

### Conclusion
The breadth of the rectangle is 10 cm.

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