What must be the length (in cm) of the diagonal of a rectangle if its area and breadth are `120 cm^(2)` and 8 cm respectively ?

Options

A. 34
B. 17
C. 15
D. 30

Answer

To find the length of the diagonal of a rectangle given its area and breadth, we can follow these steps:

### Step 1: Identify the known values
- Area of the rectangle (A) = 120 cm²
- Breadth (b) = 8 cm

### Step 2: Use the formula for the area of a rectangle
The area of a rectangle is given by the formula:
\[ A = \text{Length} \times \text{Breadth} \]
From this, we can express the length (L) in terms of area and breadth:
\[ L = \frac{A}{b} \]

### Step 3: Calculate the length
Substituting the known values into the formula:
\[ L = \frac{120 \text{ cm}^2}{8 \text{ cm}} = 15 \text{ cm} \]

### Step 4: Use the Pythagorean theorem to find the diagonal
The diagonal (D) of a rectangle can be calculated using the Pythagorean theorem:
\[ D = \sqrt{L^2 + b^2} \]

### Step 5: Substitute the values of length and breadth
Now, substituting the values we found:
\[ D = \sqrt{(15 \text{ cm})^2 + (8 \text{ cm})^2} \]
\[ D = \sqrt{225 \text{ cm}^2 + 64 \text{ cm}^2} \]
\[ D = \sqrt{289 \text{ cm}^2} \]

### Step 6: Calculate the diagonal
Taking the square root:
\[ D = 17 \text{ cm} \]

### Final Answer
The length of the diagonal of the rectangle is **17 cm**.

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