A rectangular garden must have a perimeter of 150 feet and an area of at least 1200 square feet. describe the possible lengths of the garden. round your answers to the nearest foot.

Answer: 51.86 and 23.14Step-by-step explanation:The rectangular garden must have a perimeter of 150 feetPerimeter of rectangular garden =2l + 2w=150 -----------1The rectangular garden must have a perimeter of 150 feet and an area of at least 1200 square feet.Area of rectangular garden = l×w= 1200 feet^2 -----------2From equation 2, l=1200/wPut l=1200/w in equation 12× 1200/w + 2w = 150(2400/w) +2w = 150(2400+2w^2)/w =1502400+2w^2= 150w2w^2- 150w+2400=0Using the general formulaw = [-b+-√(b^2-4ac)]/2aa = 2, b =-150, c=2400w =[--150+/-√(-150^2-4×2×2400)]/2×2=[150+/-√(22500-19200)]/4=[150+/-√3300)]/4=(150+57.45)/4 or (150-57.45)/4w= 207.45/4 or 92.55/4w= 51.86 or w= 23.14l = 1200/51.86 or l= 1200/23.14l = 23.14. or l= 51.86For an area of at least 1200ft^2The dimensions are 51.86 and 23.14