Question

Find the dimensions for the cuboid whose volume is 5x²-25

Answer 1

Volume of a cuboid is given by : V = l×b×h

here V = 5x^2 - 25
which can be written after taking 5 as common outside as
V = 5(x^2 - 5)

now consider (x^2 - 5)
it is of the form (a^2 - b^2)
Where a= x and b=root 5
(a^2 - b^2) = (a+b)(a-b)
so (x^2 - 5) =
(x+ root 5)×(x - root 5)

Therefore :
V = 5 × (x+ root 5 ) × ( x - root 5 )

therefore the dimension l, b and h are
l =5
b = (x + root 5)
h = ( x - root 5)

where l,b and h are length,breadth and height respectivrly.