Question

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?

Answer 1

Try this solution (this is not the shortest way!).

Note, the length of the diagonal is 45 cm.=4,5 dm.

Answer: the side is 22.5 cm., the EF is 12 cm.

Answer 2

Explanation:

area of rhombus = base x height or diagonal 1 x diagonal 2 / 2

one diagonal = 4.5dm = 45cm

the other diagonal = 540 / 45 * 2 = 24cm

the diagonals in a rhombus are perpendicular 2 each other

so half diagonals and one side of the rhombus form a right-angled triangle

side^2 = half-diagonal 1^2 + half-diagonal 2^2

= (45/2)^2 + (24/2)^2

= 650.25

side = sqrt (650.25) = 25.5cm

540 = height x side

height = 540 / 25.5 = 21.1765cm

distance between the point of intersection of the diagonals and the side of the rhombus = height / 2 = 10.59cm