SOLUTION: What is the perimeter of a rhombus whose diagonals are 16 and 30?

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Question 951145: What is the perimeter of a rhombus whose diagonals are 16 and 30?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The four sides of a rhombus have equal measures. Let each side have length x.
Then the perimeter of the rhombus will be P=4x
given:
d%5B1%5D=16
d%5B2%5D=30
diagonals of a rhombus are perpendicular and divide a rhombus into 4 right angle triangles
each of right angle triangles has one leg equal to half of the length of one diagonal and the other leg is half of the length of one diagonal, and hypothenuse is the side of the rhombus
so, x%5E2=%28d%5B1%5D%2F2%29%5E2%2B%28d%5B2%5D%2F2%29%5E2......plug in given values for diagonals

x%5E2=%2816%2F2%29%5E2%2B%2830%2F2%29%5E2
x%5E2=8%5E2%2B15%5E2
x%5E2=64%2B225
x%5E2=289
x=sqrt%28289%29
x=17
Then the perimeter of the rhombus will be:
P=4x
P=4%2A17
P=68