Nice prism

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

Result

S =  192 cm2

Solution:

a+b+c=19 a2+b2+c2=132 a=3 b=4 c=19(a+b)=19(3+4)=12 S=2 (a b+b c+c a)=2 (3 4+4 12+12 3)=192 cm2a+b+c=19 \ \\ a^2+b^2+c^2=13^2 \ \\ a=3 \ \\ b=4 \ \\ c=19-(a+b)=19-(3+4)=12 \ \\ S=2 \cdot \ (a \cdot \ b+b \cdot \ c+c \cdot \ a)=2 \cdot \ (3 \cdot \ 4+4 \cdot \ 12+12 \cdot \ 3)=192 \ \text{cm}^2



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