Question

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----

Answer 1

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.