The length of the diagonals of a rhombus is 40 cm and 60 cm. What is the length of the side of the rhombus?

Given:

Length of one diagonal of the rhombus = 40 cm

Length of the other diagonal of the rhombus = 60 cm

Formula Used:

In a rhombus, the diagonals are perpendicular bisectors of each other, and they divide the rhombus into four congruent right-angled triangles.

Let's use the Pythagorean theorem to find the length of the side of the rhombus.

Solution:

Let's denote the length of the side of the rhombus as "s" and the diagonal as d1 and d2.

According to the given information, the diagonals of the rhombus are 40 cm and 60 cm. These diagonals divide the rhombus into four congruent right-angled triangles.

Using the Pythagorean theorem, we can write the following equation for one of the right-angled triangles:

(d1/2)² + (d2/2)² = (s)²

Simplifying this equation:

(40/2)2 + (60/2)2 = (s)2

(20)2 + (30)2 = (s)2

400+ 900 = (s)2

s² = 1300

s = √1300

s = 10√13

Therefore, the length of the side of the rhombus is 10√13 cm.