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 290 feet by 80 feet.The manufacturer wants to increase each dimension by the same amount. A)A(x)= (290 - x)(80 - x)= 34,800 ft² B)A(x)= (290 - x)(80 + x)= 34,800 ft² C)A(x)= (290 + x)(80 - x)= 34,800 ft² D)A(x)= (290 + x)(80 + x)= 34,800 ft² E)A(x)= (290 - x)(80 - x)= -34,800 ft²

Question

Quizplus · Accepted Answer

To increase the floor area of the current facility by the same amount in both directions, we need to add the same amount to both dimensions. Let x be the amount added to each dimension. Then the new dimensions of the facility will be 290 + x and 80 + x. The new floor area will be the product of these two dimensions: (290 + x)(80 + x). Setting this equal to 1.5 times the current floor area (1.5*290*80) and solving for x gives (290 + x)(80 + x) = 34800. Simplifying this equation gives x^2 + 370x - 1400 = 0. Using the quadratic formula gives x = 2*(25sqrt(14)-185). This is a positive value, so it represents an increase in both dimensions. Therefore, the best choice is D.

A Manufacturer Wants to Enlarge an Existing Manufacturing Facility Such