Question

The total surface area and volume of a rectangular parallelopiped be 192 cm- and 144 cm respectively.
If the length of the diagonal be 13 cm, then find the three dimensions of the rectangular parallelopiped.​

Answer 1

║⊕ANSWER⊕║

Volume of rectangular parallel pipe = l * b * h = 144 cm …………… (1)

Surface Area = 2( lb + bh + hl ) = 192 cm²

Corner to corner diagonal  = 13 cm

l² + b² + h² = 13² = 169

Since, ( l + b + h )² = l² + b² + h² + 2( lb + bh + hl )

=> ( l+ b+ h)² = 169 + 192 = 361

=> l + b + h = 19 …………… (2)

By ( 1) & (2)

l b h = 144

& l + b + h = 19

Now, since prime factors of 144 =2 x 2 x 2 x 2 x 3 x 3

Since 19 = 1+18

19 = 2+ 17

19 = 3 + 16

Or, 19 = 3 + 12 + 4 , we select 12 & 4 as 3,12,& 4 contain all the prime factors of 144

=> l x b x h = 12 x 4 x 3 = 144

& l + b + h = 12 + 4 + 3 = 19

Therefore, 3 sides.. length = 12cm

breadth = 4 cm

height = 3cm