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Provide dimensions (Posted on 2021-02-03) Difficulty: 2 of 5
A rhombus has area 64.
Its longer diagonal is twice as long as the shorter diagonal.

What is the perimeter of the rhombus?

No Solution Yet Submitted by Ady TZIDON    
Rating: 2.5000 (2 votes)

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soln Comment 1 of 1
Since its diagonals d and D divide the rhombus into 4 congruent right triangles, 
Area A = 4 [(1/2) (d/2) (D/2)] = 1/2 d D.
Since here, D = 2 d, with A = 64, we get d=8.
Side S = sqrt [(d/2)^2 + (D/2)^2] =  sqrt[(d^2)/4+d^2]=
sqrt[5 (d^2/4)] = sqrt(5) d/2 = 4 sqrt(5).  So, P = 4 S = 16 sqrt(5) 

Edited on February 3, 2021, 4:01 pm
  Posted by Steven Lord on 2021-02-03 08:07:29

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