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
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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