Question

If the lengths of the diagonals of a rhombus are 24 cm and 10 cm, then each side of the rhombus is

• A. 12 cm
• B. 14 cm
• C. 15 cm
• D. 13 cm

Answer 1

The Correct Option is D

Given: The diagonals of a rhombus are 24 cm and 10 cm. 

Step 1: Understanding the properties of a rhombus

In a rhombus, the diagonals bisect each other at right angles.

Let the diagonals be \( d_1 = 24 \) cm and \( d_2 = 10 \) cm.

Each diagonal is divided into two equal halves:

\[ \frac{d_1}{2} = \frac{24}{2} = 12 \quad \text{and} \quad \frac{d_2}{2} = \frac{10}{2} = 5 \]

Step 2: Apply Pythagoras Theorem

Each side of the rhombus forms a right-angled triangle with half-diagonals as legs:

\[ s^2 = 12^2 + 5^2 \] \[ s^2 = 144 + 25 \] \[ s^2 = 169 \] \[ s = \sqrt{169} = 13 \text{ cm} \]

Final Answer: 13 cm

Answer 2

To find the length of each side of the rhombus, we can use the properties of a rhombus in relation to its diagonals. A rhombus is a type of polygon that is a parallelogram with all sides equal in length, and its diagonals bisect each other at right angles.
Given that the diagonals are 24 cm and 10 cm, we can apply the Pythagorean theorem. The diagonals of the rhombus intersect at right angles, thus creating four right-angled triangles within the rhombus. Half of each diagonal serves as the two perpendicular sides of these triangles.

The length of each half of the diagonals are:

• Half of the first diagonal = 24 cm ÷ 2 = 12 cm
• Half of the second diagonal = 10 cm ÷ 2 = 5 cm

In one of the triangles formed, these halves of the diagonals are the two shorter sides, and one side of the rhombus is the hypotenuse.

Applying the Pythagorean theorem:

Side² = 12² + 5²

=> Side² = 144 + 25

=> Side² = 169

=> Side = √169

=> Side = 13 cm

Therefore, each side of the rhombus is 13 cm.