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Question

$$A, B, C$$ denote the areas of three co-terminus faces of a cuboid. If $$P$$ and $$S$$ denote the product and sum of dimensions of the cuboid respectively, which one of the following is correct?


A
PS=A2+B2+C2
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B
PS=AB+BC+CA
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C
P=S(A+B+C)
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D
SP=(A+B+C)2
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Solution

The correct option is B $$PS= AB + BC + CA$$
Let $$ l, b$$ and $$h $$ be the length, breadth and height of the cuboid respectively. 
Given, $$ P = lhb, S= l + b + h, A = lh, B= lb, C= bh $$
Now, $$ PS = lbh \times ( l + b + h)$$
$$ ={l}^{2}bh + l{b}^{2}h + lb{h}^{2} $$
$$ = B \times A + B \times C + A \times C $$
$$= AB + BC + AC $$

Mathematics

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