SOLUTION: ABCD is a rectangle such that AD = 2AB and the diagonal AC = root5 d the the perimeter of rectangle ABCD=?

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Question 1045516: ABCD is a rectangle such that AD = 2AB and the diagonal AC = root5 d the the perimeter of rectangle ABCD=?
Found 3 solutions by advanced_Learner, MathTherapy, ikleyn:
Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
we know AB=CD
AC=BD=sqrt%285%29
perimeter=2AC%2B2AB
let AB=x then AD=2x
you have right angle triangle
sqrt%285%29%5E2+x%5E2=%282x%29%5E2
x=sqrt%285%2F3%29
p=2%2Asqrt%285%29%2B2%2A%28sqrt%285%2F3%29%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

ABCD is a rectangle such that AD = 2AB and the diagonal AC = root5 d the the perimeter of rectangle ABCD=?

Answer by ikleyn(52784) About Me  (Show Source):
You can put this solution on YOUR website!
.
ABCD is a rectangle such that AD = 2AB and the diagonal AC = root5 d the the perimeter of rectangle ABCD=?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

We know AB=CD.

AC=BD=sqrt%285%29.

Perimeter=2AD%2B2AB.

Let AB=x.  Then AD=2x.

You have right angle triangle

x%5E2 + %282x%29%5E2 = %28sqrt%285%29%29%5E2,

5x%5E2=5,

x = 1.

Then AB = 1, AD = 2, and the perimeter = 1 + 2 + 1 + 2 = 6 units.

Answer.  The perimeter is 6 units.