An enclosed field is made up of three sections:
• One section is a 10-yard by 10-yard square.
• Another section is a larger square.
• A third section is rectangular with a width of 10 yards. It shares a side with the larger square. The total area of the enclosed field is 975 square yards.
Part 1
What is the area, in square yards, of the smallest section? (Use only the digits 0 – 9 to enter a number.)
Part 2
What is the area, in square yards, of the largest section? (Use only the digits 0 – 9 to enter a number.)
Part 3
What is the area, in square yards, of the remaining section? (Use only the digits 0 – 9 to enter a number.)
To find the answers to these questions, we need to break down the information provided and apply some basic geometry concepts. Let's solve each part step by step:
Part 1: Area of the smallest section
According to the given information, one section is a 10-yard by 10-yard square. The formula to find the area of a square is A = side^2. So, the area of the square is 10^2 = 100 square yards.
Part 2: Area of the largest section
We know that the total area of the enclosed field is 975 square yards, and we already accounted for the area of the small square (100 square yards) in Part 1. The rest of the enclosed field is made up of the larger square and the rectangular section. Let's denote the side length of the larger square as x.
We can set up an equation to find x:
Area of the larger square (x^2) + Area of the rectangular section (10 * x) = Total area (975)
x^2 + 10x = 975
Rearranging the equation:
x^2 + 10x - 975 = 0
Factoring or using the quadratic formula, we find that x = 25 or x = -39. However, since sides cannot have negative lengths, we discard x = -39.
Therefore, the side length of the larger square is 25 yards, so the area is 25^2 = 625 square yards.
Part 3: Area of the remaining section
To find the area of the remaining section, we subtract the areas of the two sections we already found from the total area of the field:
Remaining section area = Total area - Area of the small square - Area of the large square
Remaining section area = 975 - 100 - 625 = 250 square yards.
Summary of answers:
Part 1: Area of the smallest section = 100 square yards
Part 2: Area of the largest section = 625 square yards
Part 3: Area of the remaining section = 250 square yards
You know, if you want to ask a question, that's fine. But do not include instructions and warnings that may appear in your assignment.
If the larger square has side x, then the area of the strip is 10x.
Since x > 10, 10x > 100, and x^2 > 100, so the 10x10 square is the smallest section.
?? Since you give no value for x, it is hard to some up with a number for the other two sections. All we know is that their combined area is 975-100.