SOLUTION: Im trying to help a friend solve this problem n our homework, but i dont know how to solve it myself. can you help? a rhombus has a perimeter of 80 inches. the longer diagonal

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Question 1068233: Im trying to help a friend solve this problem n our homework, but i dont know how to solve it myself. can you help?
a rhombus has a perimeter of 80 inches. the longer diagonal has a length of 32 inches. why does the shorter diagonal have to be 24 inches?
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
helps to draw this
rhombus has sides of 20 cm each
longer diagonal 32 cm and is perpendicular to other diagonal.
Half of each diagonal is a leg of a right triangle with hypotenuse 20
half of the longer is 16
half of the shorter is x
their squares add to 400, the square of 20.
256+x^2=400
x^2=144
x=12, which is half the length of the shorter diagonal.
24 inches is the length of the whole shorter diagonal.
This is a 3-4-5 right triangle with all sides multiplied by 4.