The volume of a rectangular parallel pipe is given as 144 cm cube. Its surface area is given as 192 sq cm. And its corner to corner diagonal is given as 13 cm. How do I find out the three sides?
Answers
l * b * h = 144 cc …………… (1)
SA = 2( lb + bh + hl ) = 192 cm²
Corner to corner diagonal AG = 13 cm
In the above image , in right tri ABC
AC² = l² + b²
In right tri ACG
AG² = AC² + GC² = 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
So, 3 sides.. length = 12cm, breadth = 4 cm & height = 3cm
hope it helps
Answer:
Step-by-step explanation:
Volume of rectangular parallel pipe =
l * b * h = 144 cc …………… (1)
SA = 2( lb + bh + hl ) = 192 cm²
Corner to corner diagonal AG = 13 cm
In the above image , in right tri ABC
AC² = l² + b²
In right tri ACG
AG² = AC² + GC² = 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