Diagonal of a rhombus = 40cm and 42cm. What are the sides of the rhombus?

It is known from the condition that the diagonals of the rhombus are 40 cm and 42 cm. And we need to find the length of the side of the rhombus.

For this, we will consider a right-angled triangle, which is formed by the side of the rhombus and the halves of the diagonals of the rhombus.

So, the diagonals of the rhombus intersect at right angles and the intersection point is halved.

The legs of a right-angled triangle are half of the diagonals of the rhombus. Let’s find their length 40: 2 = 20 cm, 42: 2 = 21 cm.

Let’s apply the Pythagorean theorem:

c ^ 2 = a ^ 2 + b ^ 2;

c = √ (a ^ 2 + b ^ 2) = √ (20 ^ 2 + 21 ^ 2) = √ (400 + 441) = √841 = 29 cm side of the rhombus.