Precalc word problem

Question

You wish to make Suzie a rectangular feeding trough. The length is 5 cm less than 3 times the width and the height is half the width. The volume of her feeding trough is 400 cubic inches. What are the dimensions of her feeding trough? Round to the nearest centimeter.

Answer 1

width = w

 

length = 3w - 5

 

height = w/2

 

Volume = length * width * height

 

400 = (3w -5) (w)(w/2)

 

800 = 3w³   - 5w² 

 

3w³  - 5w²  -800 = 0

 

 

solving this polynomial equation

 

w= 7.042840 cm

l =3(7.042840) -5 =16.12852 cm

h =  7.042840/ 2 = 3.52142 cm

 

Answer 2

w(3w-5)(1/2)w = 400

 

w^2(3w-5) = 800

 

 3w^3 - 5w^2 - 800 = 0

 

w is approximately 7.043

 

you can find the height as 1/2w

and the length as 3w-5