The volume of a rectangular parallelepiped is given as 144 cc. 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
Answer:
all the best model of William all the time table and timing send kar uchu the
Answer:
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
So, 3 sides.. length = 12cm, breadth = 4 cm & height = 3cm
Step-by-step explanation:
I hope it's helps u thank you
