SOLUTION: The perimeter of the rhombus is 20dm and one of its longer diagonal is 8dm:calculate the length of its shorter diagonal and its area.

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Question 1160635: The perimeter of the rhombus is 20dm and one of its longer diagonal is 8dm:calculate the length of its shorter diagonal and its area.
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

rhombus.png



The sides of a rhombus are all congruent. (the same length).
AB=BC=CD=DA
The two diagonals are perpendicular, and they bisect each other. This means they cut each other in half.
AO=OC=%281%2F2%29AC, and BO=OD=%281%2F2%29BD
if he perimeter of the rhombus is 20dm , then
4AB=20dm
AB=5dm
since AB=5dm, and if its longer diagonal is AC=8dm=> %281%2F2%29+AC=4dm, then 1%2F2+of shorter diagonal is
%28OB%29%5E2=%28AB%29%5E2-%28%281%2F2%29AC%29%5E2..... substitute values from above
%28OB%29%5E2=%285dm%29%5E2-%284dm%29%5E2
%28OB%29%5E2=25dm%5E2-16dm%5E2
%28OB%29%5E2=9dm%5E2
OB=3dm->1%2F2+of shorter diagonal, so the length of its shorter diagonal BD=6dm
and its area will be:
You can find the area in square units of the rhombus by multiplying the lengths of the two diagonals and dividing by two
in your case the length of diagonals is 8dm and 6dm, so we have
A=%288dm%2A6dm%29%2F2
A=48dm%5E2%2F2
A=24dm%5E2

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

The perimeter of the rhombus is 20dm and one of its longer diagonal is 8dm:calculate the length of its shorter diagonal and its area.
Diagonals of a rhombus are PERPENDICULAR to each other.

As the rhombus' perimeter is 20 dm, each side = matrix%281%2C4%2C+20%2F4%2C+%22=%22%2C+5%2C+dm%29

A rhombus contains 4 right-triangles.

As the longer diagonal's length is 8 dm, and the diagonals of a rhombus bisect each other then each longer leg/side of each right-triangle = matrix%281%2C4%2C+8%2F2%2C+%22=%22%2C+4%2C+dm%29

Wee now have 4 right-triangles with 3-4-5 PYTHAG. TRIPLES, which means that each SHORTER side/leg of each right-triangle = 3, thus making the 

With each of the 4 right-triangles having legs of 3 dm and 4 dm, each right-triangle's area = 

As there are 4 right-triangles,