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?

1. The area of the rhombus can be found by the formula

where are rhombus's diagonals.

Note that then

2. The diagonals of rhombus are perpendicular and are bisectors of each other. Then the triangle formed with halfs of diagonals is right triangles with legs

The hypotenuse of this triangle is the rhombus's side. By the Pythagorean theorem

3. The distance between the point of intersection of the diagonals and the side of the rhombus is the height of right triangle considered above.

Use twice the Pythagorean theorem to find this height:

where x is projection of leg 12 cm and h is height.

Subtract the first equation from the second:

Then