The sides of a rhombus are 10cm long. If the lengths of the diagonals differ by 4, what is the area of the rhombus?

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- May 29th 2007, 03:44 PMjumpman23Rhombus
The sides of a rhombus are 10cm long. If the lengths of the diagonals differ by 4, what is the area of the rhombus?

- May 29th 2007, 04:58 PMSoroban
Hello, jumpman23!

Quote:

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.