perplexus.info :: Geometry : Provide dimensions

Provide dimensions (Posted on 2021-02-03)

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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