Question

Please help. It would mean a lot, I am very much confused...

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.)

Answer 1

1) 100 square yards

2) 625 square yards

3) 250 square yards

Explanation:

Let's say x is the side length of the larger square.

That means the area of the larger square is x², and the area of the rectangle is 10x. The area of the smaller square is 100 square yards.

Since the total area is 975 square yards:

x² + 10x + 100 = 975

x² + 10x − 875 = 0

(x − 25) (x + 35) = 0

x = 25 or -35

x can't be negative, so x = 25 yards.

Part 1) The smallest section is the small square. Its area is 100 square yards.

Part 2) The largest section is the large square. Its area is 25² = 625 square yards.

Part 3) The third section is the rectangle. Its area is 25×10 = 250 square yards.