The lengths of the diagonals of a rhombus are $ 10 ext{ cm}$ and $ 24 ext{ cm}$. The length of the side of t

Question

The lengths of the diagonals of a rhombus are $ 10	ext{ cm}$ and $ 24	ext{ cm}$. The length of the side of the rhombus is:

Examoogle · Accepted Answer

The correct answer is Option A: 13 cm. Remember the Pythagorean triple (5, 12, 13). Since diagonals of a rhombus bisect each other at 90°, half-diagonals are 5 and 12, forming a right triangle with hypotenuse (side) 13.

Step-by-Step Solution & Concepts:
Shortcut Trick: Remember the Pythagorean triple (5, 12, 13). Since diagonals of a rhombus bisect each other at 90°, half-diagonals are 5 and 12, forming a right triangle with hypotenuse (side) 13.

Formula Used: $$Side = \sqrt{(\frac{d_1}{2})^2 + (\frac{d_2}{2})^2}$$

Given: Diagonal lengths of a rhombus are d1 = 10 cm and d2 = 24 cm.

Steps: Identify properties: In a rhombus, diagonals bisect each other at right angles ($90^\circ$).. Calculate half-diagonals: The segments from the center to the vertices are half the diagonal lengths.. Apply Pythagorean theorem: The side of the rhombus acts as the hypotenuse of a right-angled triangle formed by the half-diagonals.. Final calculation: Extracting the square root gives the side length.

Answer: A is correct because the side of the rhombus is calculated as $\sqrt{5^2 + 12^2} = 13 	ext{ cm}$.

Exam Tip: This concept is frequently tested in coordinate geometry where you find distance between midpoints or vertices of quadrilaterals.

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