Identify Properties of a Rhombus

The diagonals of a rhombus bisect each other at right angles ($90°$), dividing the rhombus into four congruent right-angled triangles.

$\text{Angle between diagonals } = 90°$

Find the Half-Diagonals

Divide each given diagonal by 2 to get the lengths of the legs of the right-angled triangle: $\frac{14}{2} = 7$ cm and $\frac{48}{2} = 24$ cm.

$r_1 = 7 \text{ cm}, \quad r_2 = 24 \text{ cm}$

Calculate Side Length using Pythagoras Theorem

Apply the Pythagorean theorem to find the side length $s$ of the rhombus: $s = \sqrt{7^2 + 24^2} = \sqrt{49 + 576} = \sqrt{625} = 25$ cm.

$s = \sqrt{7^2 + 24^2} = 25 \text{ cm}$

Calculate the Perimeter

Since all four sides of a rhombus are equal, multiply the side length by 4 to get the total perimeter: $P = 4 \times 25 = 100$ cm.

$P = 4 \times 25 = 100 \text{ cm}$