Question

The diagonals of a rhombus are 10 centimeters and 24 centimeters. A side of the rhombus measures

Answer 1

The side length of the Rhombus is 13 cm

Here, we want to get the measure of the side length of the Rhombus

We start with a diagrammatic representation of the given information as follows;

Where AC and BD represents the diagonal lengths

Let AC = 10 cm and BD equals 24 cm

Mathematically, the diagonals bisect each other at right angles

Thus, we have it that;

$\begin{gathered} AO\text{ = }\frac{1}{2}\times AC\text{ = }\frac{1}{2}\times\text{ 10 cm = 5 cm} \\ \\ BO\text{ = }\frac{1}{2}\times\text{ BD = }\frac{1}{2}\times\text{ 24 cm = 12 cm} \end{gathered}$

Since we have a right angle, it follows that AOB is a right triangle with the side length of the rhombus being the hypitenuse as it is the side that faces the right triangle

From Pythagoras' ; the square of the hypotenuse equals the sum of the squares of the two other sides

Thus, we have it that;

$\begin{gathered} AB^2=5^2+12^2 \\ AB^2\text{ = 169} \\ AB\text{ = }\sqrt[]{169} \\ AB\text{ = 13} \end{gathered}$