Question

The diagonals of a rhombus are 16 cm and 12 cm. The side of the rhombus would be:

• A. 10 cm
• B. 11 cm
• C. 8 cm
• D. 9 cm

Hint:

In a rhombus, the diagonals bisect each other at right angles. The side length can be determined using the Pythagorean theorem, with the half-lengths of the diagonals as the legs of the right-angled triangle.

Answer 1

The Correct Option is A

Step 1: Understanding the properties of a rhombus.
In a rhombus, the diagonals bisect each other at right angles. Therefore, the two diagonals divide the rhombus into four right-angled triangles. The sides of the rhombus can be found by applying the Pythagorean theorem to these right-angled triangles.

Step 2: Apply the Pythagorean theorem.
Let the diagonals of the rhombus be p = 16 cm and q = 12 cm. Since the diagonals bisect each other, the half-lengths of the diagonals are:

p/2 = 8 cm,   q/2 = 6 cm

These halves of the diagonals are the two legs of the right-angled triangles, and the side of the rhombus is the hypotenuse. Using the Pythagorean theorem:

s² = (p/2)² + (q/2)²

s² = 8² + 6² = 64 + 36 = 100

s = √100 = 10 cm

Step 3: Conclusion.
Thus, the side length of the rhombus is 10 cm.
Therefore, the correct answer is (1) 10 cm.