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diagonal length of a rectangular parallelepiped, using the surface area and sum of edge lengths

작성자 Uploader : rainbow 작성일 Upload Date: 2019-03-08변경일 Update Date: 2019-03-11조회수 View : 311

When the surface area of a rectangular parallelepiped is S and the sum of the lengths of all the edgeis L, the length d of the diagonal line can be obtained as follows.

If the length of each side of the rectangular parallelepiped is a, b and c, those L, S and d can be expressed as follows.

L = 4*(a+b+c)

S = 2*(ab+bc+ca)

d = (a^2+b^2+c^2)^(1/2)

Meantime,

(a+b+c)^2 = a^2+b^2+c^2+2*(ab+bc+ca)

Thus, d can be expressed by L and S as below.

(a^2+b^2+c^2)^(1/2) = (a+b+c)^2 - 2*(ab+bc+ca)

d = (L/4)^2 - S


*** 참고문헌[References] ***

d = (L/4)^2 - S
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