Question

If the length of diagonals of a rhombus are 12 cm and 16 cm, then the length of the side of the rhombus will be:

• A. 20 cm
• B. 10 cm
• C. 9 cm
• D. 8 cm

Hint:

In a rhombus, the diagonals bisect each other at right angles. Use the Pythagorean theorem to find the side length.

Answer 1

The Correct Option is B

We are given a rhombus with diagonals of lengths 12 cm and 16 cm. To find the length of the side of the rhombus, we can use the property of the rhombus that states: \[ \text{Side}^2 = \left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2 \] where \( d_1 \) and \( d_2 \) are the lengths of the diagonals.
Step 1: Apply the formula.
Substitute the values for the diagonals \( d_1 = 12 \) cm and \( d_2 = 16 \) cm: \[ \text{Side}^2 = \left(\frac{12}{2}\right)^2 + \left(\frac{16}{2}\right)^2 \] \[ \text{Side}^2 = 6^2 + 8^2 = 36 + 64 = 100 \]
Step 2: Solve for the side.
Taking the square root of both sides: \[ \text{Side} = \sqrt{100} = 10 \, \text{cm} \]
Step 3: Conclusion.
Thus, the length of the side of the rhombus is 10 cm. The correct answer is (B).