Nice prism

Calculate the cuboid's surface if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm.

Correct answer:

S =  192 cm2

Step-by-step explanation:

s=19 cm u=13 cm a+b+c=s a2+b2+c2 = u2  S = 2⋅ (a⋅ b+b⋅ c+c⋅ a)  (a+b+c)2 = s2 = a2 + 2ab + 2ac + b2 + 2bc + c2 s2 = (a2 + b2 + c2) + (2ab + 2ac  + 2bc) s2 = u2 + 2ab + 2ac + 2bc s2 = u2 + S  S=s2−u2=192−132=192=192 cm2   Verifying Solution:   a=3 cm b=4 cm c=s−(a+b)=19−(3+4)=12 cm  S1​=2⋅ (a⋅ b+b⋅ c+c⋅ a)=2⋅ (3⋅ 4+4⋅ 12+12⋅ 3)=192

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