Rhombus — Perimeter from Diagonals: If the diagonals of a rhombus are 4.8 cm and 1.4 cm, find the perimeter of the rhombus (in cm).

Introduction / Context:In a rhombus, diagonals are perpendicular bisectors. Each side equals the hypotenuse of a right triangle with legs equal to half the diagonals. Once one side is known, the perimeter is four times the side length.

Given Data / Assumptions:

• d1 = 4.8 cm ⇒ d1/2 = 2.4 cm
• d2 = 1.4 cm ⇒ d2/2 = 0.7 cm
• Side s = √[(d1/2)^2 + (d2/2)^2]
• Perimeter P = 4s

Concept / Approach:Apply the Pythagorean theorem to the half-diagonals right triangle to compute the rhombus side, then multiply by 4 for the perimeter. Keep decimals precise to avoid rounding errors.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 5 cm equals the side, not the perimeter/2.
• 12 cm and 20 cm overestimate s.
• 8 cm underestimates P.

Common Pitfalls:

• Using full diagonals instead of halves within Pythagoras.

Final Answer:10 cm.