Cuboid - sum of edges length

Calculate the cuboid's dimensions if the sum of its edges is 19 cm. The body's diagonal size is 13 cm, and its volume is 144 cm3. The total surface area is 192 cm2.

Final Answer:

a =  3 cm
b =  4 cm
c =  12 cm

Step-by-step explanation:

d=13 cm V=144 cm3  a+b+c=19 a2+b2+c2 = d2 = 132 V=abc 144 = 2 × 2 × 2 × 2 × 3 × 3 = 24 × 32 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3 = 26 × 3  a=3=3 cm  A=V/a=144/3=48 cm2 A=48 = 2 × 2 × 2 × 2 × 3 = 24 × 3  b=22=4 cm c=22⋅ 3=12 cm   Verifying Solution:  S1​=2⋅ (a⋅ b+b⋅ c+c⋅ a)=2⋅ (3⋅ 4+4⋅ 12+12⋅ 3)=192 cm2 V1​=a⋅ b⋅ c=3⋅ 4⋅ 12=144 cm3 d1​=a2+b2+c2​=32+42+122​=13 cm s1​=a+b+c=3+4+12=19 cm

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