The area of a rhombus is 840 `cm^2` and one of its diagonals is 14 cm, find the other diagonal.

Options

A. 100 cm
B. 140 cm
C. 120 cm
D. 210 cm

Answer

To find the other diagonal of the rhombus, we can use the formula for the area of a rhombus, which is given by:

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

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

### Step 1: Identify the known values
We know:
- The area of the rhombus = 840 cm²
- One diagonal (\(d_1\)) = 14 cm

### Step 2: Set up the equation
Using the area formula, we can substitute the known values into the equation:

\[ 840 = \frac{1}{2} \times 14 \times d_2 \]

### Step 3: Simplify the equation
To eliminate the fraction, we can multiply both sides by 2:

\[ 2 \times 840 = 14 \times d_2 \]

This simplifies to:

\[ 1680 = 14 \times d_2 \]

### Step 4: Solve for the other diagonal (\(d_2\))
Now, we can solve for \(d_2\) by dividing both sides by 14:

\[ d_2 = \frac{1680}{14} \]

### Step 5: Calculate the value
Now we perform the division:

\[ d_2 = 120 \text{ cm} \]

### Conclusion
The length of the other diagonal is \(d_2 = 120 \text{ cm}\).

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