A rhombus has diagonals of lengths 12\text{ cm} and 16\text{ cm}. What is the perimeter of… — JAMB UTME

A rhombus has diagonals of lengths $12\text{ cm}$ and $16\text{ cm}$ . What is the perimeter of the rhombus in $\text{cm}$ ?

Answer: 40 cm

Answer

The perimeter of the rhombus is

40\text{ cm}

The diagonals of a rhombus bisect each other at right angles, dividing the rhombus into four congruent right-angled triangles. Each triangle has legs measuring

6\text{ cm}

and

8\text{ cm}

. Applying the Pythagorean theorem, the hypotenuse (which is the side length of the rhombus) is

\sqrt{6^2 + 8^2} = \sqrt{100} = 10\text{ cm}

. Since all four sides of a rhombus are equal, the perimeter is

4 \times 10 = 40\text{ cm}

Step-by-Step Solution

Calculate the lengths of the semi-diagonals

The semi-diagonals are

6\text{ cm}

and

8\text{ cm}

The diagonals of a rhombus bisect each other perpendicularly.

Determine the side length of the rhombus using the Pythagorean theorem

Side length

s = \sqrt{6^2 + 8^2} = \sqrt{100} = 10\text{ cm}

Each side of the rhombus forms the hypotenuse of a right-angled triangle formed by the semi-diagonals.

Calculate the total perimeter

Perimeter

P = 4 \times 10 = 40\text{ cm}

All four sides of a rhombus are equal in length.

Key Concept

Perimeter of a rhombus derived from diagonal lengths using right-triangle properties

Estimated Time:1m 0s

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