Question 1021119: Okay so on my worksheet, it says that a rhombus has diagonals of 14 and 2x+7y-3. Then it also says that the diagonal that is 2x+7y-3 is split into two and one side of that is 3x and the other 5y-1. So with that being said, how would you find the perimeter of the rhombus?
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! The properties of the diagonals of a rhombus that we will use are:
1) The diagonals bisect each other
2) The intersection of the diagonals form 90 degree angles, that is, they are perpendicular to each other
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We can use 1 and 2 along with the Pythagorean Theorem to find the length of a side of the Rhombus
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let s be the length of a side, along with what we are given
:
3) 3x = 5y - 1
4) 3x + 5y -1 = 2x + 7y -3
:
solve equation 4 for x
x = 2y-2
:
substitute for x in equation 3
6y - 6 = 5y - 1
y = 5
x = 8
:
7^2 + (3x)^2 = s^2
49 + 576 = s^2
s = sqrt(625) = 25
:
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Perimeter of rhombus = 4s = 100
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