The length of a side of a cube can be determined
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Since and
, we can rewrite the right side of the equation as
Using the identity , we can subtract
from either side to obtain the identity
substituting that into our previous expression, the right side of our equation simply becomes
We can now write our whole equation as
Adding 2 to both sides:
dividing both sides by 3:
When 0 ≤ x ≤ π, tan x can only be equal to 1 when sin x = cos x, which happens at x = π/4, and it can only be equal to -1 when -sin x = cos x, which happens at x = 3π/4
Length of room, l = 3x + 1 ft.
Breadth of room, b = x² -1 ft.
Now, it is given that university wants each room to have 195 ft² of living space.
So,
So, above equation has two complex root and one real root i.e x = 4.08 ft .
Therefore, Length of room is 13.24 ft and breadth is 15.65 ft.
Hence, this is the required solution.