SOLUTION: Here is my question: A rhombus ABCD has a perimeter of 32cm and a diagonal AC of length 8cm. What is the exact length of diagonal BD? Thank you very much! :)

Algebra ->  Polygons -> SOLUTION: Here is my question: A rhombus ABCD has a perimeter of 32cm and a diagonal AC of length 8cm. What is the exact length of diagonal BD? Thank you very much! :)      Log On


   

Question 976283: Here is my question:
A rhombus ABCD has a perimeter of 32cm and a diagonal AC of length 8cm. What is the exact length of diagonal BD?
Thank you very much! :)
Answer by dkppathak(439) About Me  (Show Source):
You can put this solution on YOUR website!
A rhombus ABCD has a perimeter of 32cm and a diagonal AC of length 8cm. What is the exact length of diagonal BD?
perimeter of rhombus =32 let side of rhombus is a than perimeter will be 4a
4a=32
a=8
diagonal of rhombus bisect each other at 90 degree let other diagonal 2x
1/2 of given diagonal will be =1/2 of 8= 4 cm and 1/2 of other diagonal will be x
using Pythagoras theorem
8^2= X^2+4^2
64-16=x^2
48=x^2
X=sqrt of 48= 4 sqrt3
length of other diagonal will be 2x= 8sqrt3