The area and the length of one of the diagonals of a rhombus are `84 cm^(2)` and 7 cm respectively. Find the length of its other diagonals (in cm).

Options

A. 12
B. 24
C. 48
D. 36

Answer

To find the length of the other diagonal of the rhombus, we can use the formula for the area of a rhombus in terms of its diagonals. The area \( A \) of a rhombus can be calculated using the formula:

\[ A = \frac{1}{2} \times d_1 \times d_2 \]

where \( d_1 \) and \( d_2 \) are the lengths of the diagonals.

### Step 1: Identify the known values
From the question, we know:
- The area \( A = 84 \, \text{cm}^2 \)
- One diagonal \( d_1 = 7 \, \text{cm} \)

We need to find the length of the other diagonal \( d_2 \).

### Step 2: Substitute the known values into the area formula
We can rearrange the area formula to solve for \( d_2 \):

\[ 84 = \frac{1}{2} \times 7 \times d_2 \]

### Step 3: Simplify the equation
Multiply both sides by 2 to eliminate the fraction:

\[ 168 = 7 \times d_2 \]

### Step 4: Solve for \( d_2 \)
Now, divide both sides by 7:

\[ d_2 = \frac{168}{7} \]

Calculating this gives:

\[ d_2 = 24 \, \text{cm} \]

### Conclusion
The length of the other diagonal \( d_2 \) is \( 24 \, \text{cm} \).

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