An architect wants to build a scale model of a building that is in the shape of a rectangular prism. The building has a height of 45 ft., a width of 90 ft., and a length of 300 ft. The scale model is 10% of the size of the building based off its length and width, so the length of the scale model is and the width of the scale model is

Since, the area of the rectangular base =

We have to determine the width if length is (3x+1)

Let us split the middle terms of the given equation to find its factors.

Taking common from first, second and third, fourth terms.

= 3x(4x-5)+1(4x-5)

= (3x+1) (4x-5)

Since, (3x+1) is the length of the rectangular base.

Therefore, the width of the rectangular base is (4x-5) units.

Now, Volume of the rectangular prism is given by the polynomial

We have to find width and height.

Let x = -  in the given equation of volume.

We get as,

-135+135=0

Hence, (3x+1) is a factor of the given volume polynomial.

Now, performing long division of the given polynomial by (3x+1),

we get factors as (4x-5) and (2x-3).

So, the width is (4x-5) units and height is (2x-3) units.