A rhombus has area 64.

Its longer diagonal is twice as long as the shorter diagonal.

What is the perimeter of the rhombus?

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**