Question 894065: A rhombus has a side measuring 15 yards.If one of its diagonal measures 22 yards and it's area is 396 sq. yards,find the measure of the other diagonal and it's perimeter
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! something is not right with your rhombus.
the area of a rhombus is equal to d1 * d2 / 2.
d1 is one of the diagonals of the rhombus.
d2 is the other of the diagonals of the rhombus.
you know that one of the diagonals is equal to 22.
you know that the area is equal to 396.
you can use the formula to find the length of the other diagonal.
the formula becomes 396 = 22 * x / 2
multiply both sides of this equation by 2 and divide both sides of this equation by 22 to get:
396 * 2 / 22 = x which makes x = 36.
one of your diagonals is 36 and one of them is 22.
unfortunately this doesn't track with other information you know about the rhombus.
in a rhombus, all sides are equal.
if one side is 15, then the other 3 sides are 15 each.
the perimeter of your rhombus has to be equal to 60.
that's not the problem.
the problem is in the right triangles that are formed.
the diagonals of the rhombus form right angles with each other and bisect each other.
you get 4 right triangle formed, each of which has a leg of 11 and a leg of 18 and a hypotenuse of 15.
this is an impossibility because pythagorus says that the sum of the squares of the legs must be equal to the square of the hypotenuse.
15 is the hypotenuse.
18^2 + 11^2 is not equal to 15^2.
do the math and you get 445 = 225
this is not a true statement so one of the legs has to have a wrong measure.
since you are given that one of the legs will be 11 (one half of 22 is 11), then the problem must be with the other leg, or with the area.
to make a long story short, the numbers don't check out and something is wrong with your rhombus which prevents you from getting an answer that makes sense when compared to the other measurements of the rhombus.
all these properties of a rhombus should check out and they don't.
here's some information for a rhombus that might help you to understand what i'm talking about.
http://www.coolmath.com/reference/rhombus.html
here's a rhombus where everything agrees.
the sides of the rhombus are 5.
the diagonals measure 8 and 6 across.
the area of the rhombus is equal to (d1 * d2) / 2 = (8*6)/2 = 24
the rhombus forms 4 right triangles with legs of 3 and 4 each and a hypotenuse of 5.
using the area of the triangles method, the area of the rhombus is equal to 4 * 1/2 * 3 * 4 which is equal to 2 * 3 * 4 which is equal to 6 * 4 which is equal to 24.
the area based on the right triangles agrees with the area based on the diagonals.
no problem with this rhombus.
the two formulas have to agree with each other.
if they don't then there's something wrong with the measurements given for the rhombus.
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