Hello, jumpman23!
The sides of a rhombus are 10cm long.
If the lengths of the diagonals differ by 4, what is the area of the rhombus?
You're expected to know a few facts about a rhombus.
. . The diagonals of a rhombus are perpendicular.
. . If the diagonals are and , the area is: . Code:
A 10 B
* - - - - - *
/ * * /
/ * * /
10/ *O / 10
/ * * /
/ * * /
* - - - - - *
D 10 C
We have: .
Let . .Then
Then: .
In right triangle
. . so we have: .
. . which simplifies to: .
. . which factors: .
. . and has roots: .
The diagonals are: .
Therefore, the area is: . cm².