The diagonal and breadth of a rectangle is 10 ems. and 6 cms. respectively. What is the perimeter of the rectangle ?

Options

A. 32 cms
B. 28 cms
C. 27 cms
D. Cannot be determined

Answer

To find the perimeter of the rectangle given the diagonal and breadth, we can follow these steps:

### Step 1: Identify the given values
- Diagonal (AC) = 10 cm
- Breadth (BC) = 6 cm

### Step 2: Use the Pythagorean theorem
In a rectangle, the diagonal forms a right triangle with the length and breadth. According to the Pythagorean theorem:
\[ AC^2 = AB^2 + BC^2 \]
Where:
- \( AC \) is the diagonal,
- \( AB \) is the length,
- \( BC \) is the breadth.

### Step 3: Substitute the known values into the equation
\[ 10^2 = AB^2 + 6^2 \]
\[ 100 = AB^2 + 36 \]

### Step 4: Solve for the length (AB)
Rearranging the equation gives:
\[ AB^2 = 100 - 36 \]
\[ AB^2 = 64 \]

Taking the square root of both sides:
\[ AB = \sqrt{64} \]
\[ AB = 8 \, \text{cm} \]

### Step 5: Calculate the perimeter of the rectangle
The formula for the perimeter (P) of a rectangle is:
\[ P = 2 \times (Length + Breadth) \]
Substituting the values we have:
\[ P = 2 \times (8 \, \text{cm} + 6 \, \text{cm}) \]
\[ P = 2 \times 14 \, \text{cm} \]
\[ P = 28 \, \text{cm} \]

### Final Answer
The perimeter of the rectangle is **28 cm**.

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