The length of one side of a rhombus is 6.5 and its altitude is 10 cm. If the length of its diagonal be 26 cm, the length of the other diagonal will be :

Options

A. 5 cm
B. 10 cm
C. 6.5 cm
D. 26 cm

Answer

To find the length of the other diagonal of the rhombus, we can follow these steps:

### Step 1: Understand the properties of a rhombus
A rhombus has two diagonals that bisect each other at right angles. The area of the rhombus can be calculated using the formula:
\[ \text{Area} = \frac{1}{2} \times d_1 \times d_2 \]
where \(d_1\) and \(d_2\) are the lengths of the diagonals.

### Step 2: Calculate the area using the altitude
The area of the rhombus can also be calculated using the formula:
\[ \text{Area} = \text{base} \times \text{height} \]
In this case, the base is the length of one side of the rhombus, which is 6.5 cm, and the height (altitude) is 10 cm. Therefore, the area can be calculated as:
\[ \text{Area} = 6.5 \times 10 = 65 \text{ cm}^2 \]

### Step 3: Set up the equation using the diagonals
We know one diagonal \(d_1 = 26\) cm and we need to find the other diagonal \(d_2\). Using the area formula with diagonals, we have:
\[ \text{Area} = \frac{1}{2} \times d_1 \times d_2 \]
Substituting the known values:
\[ 65 = \frac{1}{2} \times 26 \times d_2 \]

### Step 4: Solve for \(d_2\)
First, simplify the equation:
\[ 65 = 13 \times d_2 \]
Now, divide both sides by 13 to find \(d_2\):
\[ d_2 = \frac{65}{13} = 5 \text{ cm} \]

### Final Answer
The length of the other diagonal \(d_2\) is 5 cm.

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