The area of the rhombus is 540 cm2; the length of one of its diagonals is 4.5 dm. what is the distance between the point of intersection of the diagonals and the side of the rhombus?

Given: Area of rhombus is 540 square cm and the length of one of its diagonals is 4.5 dm

To find the other diagonal of the rhombus:

Using formula of Area of rhombus:

Area of rhombus(A) =  ......[1]; where are the diagonals and A is the area of rhombus respectively.

Use conversion:

1 dm = 10 cm

then;

4.5 dm = cm

Substitute the value of A = 540 square cm and in [1] we have;

or

Divide by 45 both sides we get;

The distance between the point of intersection of the diagonals and the side of the rhombus :

The line perpendicular to the rhombus side i,e x the altitude to the hypotenuse of one of those right triangles.

The length x of such an altitude in a right triangle with leg lengths  and can be found from:

then:

or

or

Simplify:

x ≈ 10.59

Therefore, the distance between the point of intersection of the diagonals and the side of the rhombus is, 10.59 cm