fencing 9.5 17

Question

A security fence encloses a rectangular area on one side of a park in a city. Three sides of fencing are? used, since the fourth side of the area is formed by a building. The enclosed area measures
1152
square feet. Exactly
96
feet of fencing is used to fence in three sides of this rectangle. What are the possible dimensions that could have been used to construct this? area?

Answer 1

Let l, w be the dimensions of the rectangle.

 

Now area = A = l * w = 1152 and the fencing on the other 3 sides are l + 2w = 96

 

Now l = 96 - 2w.  Substitute this into the other equations => l * w = (96 - 2w) * w = 1152

 

                                                                                            => w² - 48w + 576 = 0

 

                                                                                            => (w - 24)² = 0

From this w = 24, which means l = 48

 

Answer 2

96/4=24

24+24=48

24*48=1152 sq ft

24 by 48 by 24 by "the building"

the maximum area of any rectangle occurs when the rectangle is a square