SOLUTION: The area of the rhombus is 480 cm2; the length of one of its diagonals is 4.8 dm. What is the distance between the point of intersection of the diagonals and the side of the rhombu

Algebra ->  Parallelograms -> SOLUTION: The area of the rhombus is 480 cm2; the length of one of its diagonals is 4.8 dm. What is the distance between the point of intersection of the diagonals and the side of the rhombu      Log On


   

Question 1075076: The area of the rhombus is 480 cm2; the length of one of its diagonals is 4.8 dm. What is the distance between the point of intersection of the diagonals and the side of the rhombus?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Here is the rhombus with its diagonals.
I put the rhombus inside a rectangular box for safekeeping,
because it looked breakable.
(I know it is not drawn to scale).

You can see that the diagonals split the rhombus into
4 congruent right triangles.
Maybe you want to know the distance x (in cm)
between the point of intersection of the diagonals and
the end of the other diagonal
(which is half of the length of the other diagonal).
It is useful to calculate that length, anyway.
The area of a rhombus is
the length of one diagonal times half the length of the other.
So, 48%2Ax=480 ---> x=10 .

Maybe you really wanted the distance between the point of intersection of the diagonals and the side of the rhombus,
measured along the shortest path, the line perpendicular to the red side.
That is f ,
the altitude to the hypotenuse of one of those right triangles.
The length f of such an altitude
in a right triangle with leg lengths a and b
can be found from
1%2Ff%5E2=1%2Fa%5E2%2B1%2Fb%5E2 .
In this case,

1%2Ff%5E2=169%2F%2825%2A576%29 --> f%5E2=25%2A576%2F169 --> f=sqrt%2825%2A576%29%2Fsqrt%28169%29=5%2A24%2F13 --> highlight%28f=120%2F13%29 .
In other words, the distance from the center of the rhombus
to one of its sides is approximately highlight%289.23cm%29 .