Question 1172893: A rectangular field has an area of 1200 square feet. The length of the field is 50ft. How wide is the field? If the field is divided into 3 rectangles (if 50ft long and 3 rectangles are x ft, 3x ft and 2x ft what would the equation be and what are the dimensions of each rectangle?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! L*w=area ft*ft=ft^2
L*W=1200 ft^2, the ^ is the exponent, so ^2 means ft*ft, multiply by itself. ft^3 is ft*ft*ft, used in volume.
50w=1200 . The units have to match on each side of the equation, so 50 ft*w ft=1200 ft*ft or ft^2. You will see square feet more than ft^2, but they are the same. Houses are rated in how many square feet they have.
w=24 ft, because I divided 1200/50 and ft*ft/ft= ft or ft^1. Anything raised to the first power is itself. The point is if you get the units right, you will often know where to put the numbers.
Draw the field out, and there will be two long sides of 50 feet each, and they are 24 feet apart at each end. The rectangles are 50 feet long, and there are two wires, fences, posts something across the 24 feet dividing the field into 3 rectangles. Each has a long side of 50 feet, but the short side has been divided up.
How is it divided? It is 24 feet, and the division is x feet, 3x feet, and 2x feet. How much is x? Well, we know that the sum of those is 6x ft. and that equals the total width of 24 feet. So dividing 24 by 6 and x is 4 feet.
One rectangle is 4 feet wide and 50 feet long. One more is 12 feet wide because it is 3x wide, and 50 feet long. The third takes what is left over, and since we have used 4 and 12 feet (total 16 feet), there are only 8 feet left over, which happens also to be 2x (it better be), and that rectangle is 50 feet long by 8 feet wide.
dividing the width into x 3x and 2x (sum 6x) means that x=4 feet, because the sum (6x) = width (24 feet)
so rectangle A would be 50 x 4
B would be 50 X 12
C would be 50 X 8 units feet for each
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