Question : If the sum of the dimensions of a rectangular parallelepiped is 24 cm and the length of the diagonal is 15 cm, then the total surface area is:
Option 1: 420 cm2
Option 2: 275 cm2
Option 3: 351 cm2
Option 4: 378 cm2
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Correct Answer: 351 cm 2
Solution : Let length = $a$ cm, breadth = $b$ cm , height = $c$ cm The sum of the dimensions of a rectangular parallelepiped = 24 cm ⇒ $a+b+c$ = 24 cm Diagonal = 15 cm ⇒ $\sqrt{a^{2}+b^{2}+c^{2}}$ = 15 cm ⇒ $a^{2}+b^{2}+c^{2}$ = 225 cm $(a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2(ab+bc+ca)$ ⇒ 576 = 225 + $2(ab+bc+ca)$ Total surface area = $2(ab+bc+ca)$ = 576 – 225 = 351 cm 2 Hence, the correct answer is 351 cm 2 .
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