Question : If the sum of the length, breadth and height of a rectangular parallelepiped is 24 cm and the length of its diagonal is 15 cm, then its total surface area is:
Option 1: 256 cm2
Option 2: 265 cm2
Option 3: 315 cm2
Option 4: 351 cm2
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Correct Answer: 351 cm 2
Solution : Given: The sum of the length, breadth and height of a rectangular parallelepiped is 24 cm and the length of its diagonal is 15 cm. Let $l,b,$ and $h$ be the length, breadth and height of the rectangular parallelepiped. Total surface area = $2(lb+bh+hl)$ Length of diagonal = $\sqrt{l^2+b^2+h^2}$ According to the question, $\sqrt{l^2+b^2+h^2}=15$ $⇒(l^2+b^2+h^2) = 225$ Also, ($l+b+h$) = 24 $⇒(l+b+h)^2 = 24^2$ $⇒l^2+b^2+h^2+2 (lb+bh+hl) = 576$ $\therefore 2(lb+bh+hl)=576 - 225=351$ cm 2 Hence, the correct answer is 351 cm 2 .
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