Question

each side of a rhombus is 61 cm and one of its diagonal is 22 cm long find the length of the Other diagonal and the area of the Rhombus​

Answer 1

Answer:

Length of the other Diagonal = 120 cm

Area of any rhombus $= 1,320 cm^2$

Step-by-step explanation:

The diagonals of any rhombus perpendicularly bisect each other.

Therefore, we get right angled triangles with the rhombus' side as hypotenuse and half of each of the diagonals as the other two sides of the right angled triangle.

Let's assume that, the length of the other diagonal is x cm.

Therefore, by pythagoras's theorem:

$(\frac{x}{2} )^2 + (\frac{22}{2} )^2 = 61^2$

$=>\frac{x^2}{4} = 61^2 - 11^2 = (61+11)(61-11) = 72*50$

$=>x^2 = 72.50.4 =72.200 = 14400 = 120^2$

∴ x = 120.

Area of any rhombus $=\frac{1}{2}$  the products of the lengths of it's Diagonals

$=\frac{1}{2} . 22 . 120 cm^2 = 11*120 cm^2 = 1,320 cm^2$