The diagonals of a rhombus are 8cm and 15cm respectively. The perimeter (in cm) of the rhombus:

Options

A. a. 60
B. b. 120
C. c. 68
D. d. 34

Answer

To find the perimeter of a rhombus when the lengths of its diagonals are given, we can follow these steps:

### Step 1: Identify the lengths of the diagonals
Let the lengths of the diagonals be:
- Diagonal 1 (d1) = 8 cm
- Diagonal 2 (d2) = 15 cm

### Step 2: Use the relationship between the diagonals and the sides of the rhombus
The relationship between the diagonals and the side of a rhombus is given by the formula:
\[ d1^2 + d2^2 = 4a^2 \]
where \( a \) is the length of a side of the rhombus.

### Step 3: Substitute the values of the diagonals into the formula
Substituting the values of the diagonals into the formula:
\[ 8^2 + 15^2 = 4a^2 \]

### Step 4: Calculate the squares of the diagonals
Calculating the squares:
\[ 8^2 = 64 \]
\[ 15^2 = 225 \]

### Step 5: Add the squares of the diagonals
Now, add the squares:
\[ 64 + 225 = 289 \]
So, we have:
\[ 289 = 4a^2 \]

### Step 6: Solve for \( a^2 \)
To find \( a^2 \), divide both sides by 4:
\[ a^2 = \frac{289}{4} \]

### Step 7: Take the square root to find \( a \)
Now, take the square root of both sides:
\[ a = \sqrt{\frac{289}{4}} = \frac{\sqrt{289}}{\sqrt{4}} = \frac{17}{2} \]

### Step 8: Calculate the side length
Thus, the side length \( a \) is:
\[ a = 17 \text{ cm} \]

### Step 9: Calculate the perimeter
The perimeter \( P \) of the rhombus is given by:
\[ P = 4a \]
Substituting the value of \( a \):
\[ P = 4 \times 17 = 68 \text{ cm} \]

### Final Answer
The perimeter of the rhombus is **68 cm**.

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