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.