We are given a rhombus with diagonals of length 12 cm and 5 cm. We need to find the perimeter of the rhombus.

1. Problem Description

We are given a rhombus with diagonals of length 12 cm and 5 cm. We need to find the perimeter of the rhombus.

2. Solution Steps

A rhombus is a quadrilateral with all four sides equal in length. The diagonals of a rhombus bisect each other at right angles. Therefore, the diagonals divide the rhombus into four congruent right-angled triangles.

Let $d_1$ and $d_2$ be the lengths of the diagonals.

Then $d_1 = 12$ cm and $d_2 = 5$ cm.

The diagonals bisect each other, so the lengths of the legs of each right-angled triangle are $d_1/2$ and $d_2/2$. In our case, $12/2 = 6$ cm and $5/2 = 2.5$ cm.

Let $s$ be the side length of the rhombus. We can use the Pythagorean theorem to find the side length $s$ of the rhombus.

$s^2 = (d_1/2)^2 + (d_2/2)^2$

$s^2 = (6)^2 + (2.5)^2$

$s^2 = 36 + 6.25$

$s^2 = 42.25$

$s = \sqrt{42.25}$

$s = 6.5$ cm

The perimeter $P$ of the rhombus is given by $P = 4s$.

$P = 4 \times 6.5$

$P = 26$ cm

3. Final Answer

The perimeter of the rhombus is 26 cm.

The correct answer is A. 26 cm.