# How to find the side of a rhombus if two diagonals of 14 and 48 cm are known

To begin with, let’s write down the conditions of the problem – let’s formulate it.

Given: Rhombus, d1 = 14 cm, d2 = 48 cm.

Find: side of rhombus =?

Solution:

1) Let’s push away from the known facts. We know the property of the rhombus, which says that the diagonals of the rhombus are perpendicular.

2) Also, do not forget the fact that the diagonals at the intersection point are divided in half.

3) Based on this, we can conclude that the halves of the diagonals of the rhombus form a right-angled triangle with the side of the rhombus.

4) This means that we can find the value of the side by the Pythagorean theorem.

5) Let AB be the desired side, then AB² = (1 \ 2 * d1) ² + (1 \ 2 * d2) ².

6) We transform the formula: AB = √ (1 \ 2 * d1) ² + (1 \ 2 * d2) ².

5) Substitute the values we know: AB = √ (1 \ 2 * 14) ² + (1 \ 2 * 48) ².

6) Perform the actions in brackets:

1.1 \ 2 * 14 = 7.

2.1 \ 2 * 48 = 24.

7) AB = √7² + 24².

8) Let’s square the numbers:

1.7² = 49.

2.24² = 576.

9) AB = √49 + 576.

10) Perform the addition: AB = √625.

11) Let’s extract the root: AB = 25 cm.

Answer: the side of the rhombus is 25 cm.