Question

A university wants to build a new residence hall with dorm rooms. The length is 3x+1 ft and the width is x^2-1 ft. If the university wants each room to have 195ft^2 of living space, what should be the dimensions of each dorm room? ["living space confuses me because idk if it's volume or bottom surface area]

Answer 1

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,

$lb = A\\\\(x^2-1)(3x+1)=195\\\\3x^3+x^2-6x-1=195\\\\3x^3+x^2-6x-196=0$

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.