SOLUTION: A manufacturer wants to enlarge an existing manufacturing facility such that the total floor area is 1.5 times that of the current facility. The floor area of the current facility

Question 1206407: A manufacturer wants to enlarge an existing manufacturing facility such that the total floor area is 1.5 times that of the current facility. The floor area of the current facility is rectangular and measures 200 feet (length) by 120 feet (width). The manufacturer wants to increase each dimension by the same amount.
(a) Write a function that represents the new floor area A. (Use x as the variable.)
A =

(b) Find the dimensions of the new floor. (Round your answers to two decimal places.)
ft (smaller value)
ft (larger value)
(c) Another alternative is to increase the current floor's length by an amount that is twice an increase in the floor's width. The total floor area is 1.5 times that of the current facility. Repeat parts (a) and (b) using these criteria.
Write a function that represents the new floor area A. (Use x as a variable.)
A =

Find the dimensions of the new floor. (Round your answers to two decimal places.)
ft (smaller value)
ft (larger value)

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

x = increase in width and length

(a) A(x) = (200+x)(120+x)

(b) The new area is 1.5 times the old area:

(200+x)(120+x)=1.5(200)(120)

The answer is not a "nice" number; you won't find it by factoring; and the quadratic formula with these large numbers is cumbersome. Use a graphing calculator or some other method to find x and then answer the question.

(c) Here the increase in the length of the floor is twice the increase in the width, so the amounts of increase are 2x and x:

A(x) = (200+2x)(120+x)

(200+2x)(120+x)=1.5(200)(120)

Use a similar method to finish.

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