Part A: The area of a square is (9a2 - 24a + 16) square units. Determine the length of each side of the

Part B: The area of a rectangle is (25a? - 3662) square units. Determine the dimensions of the rectang

Part A

Length of each side of the square = (3a - 4)

Part B

Dimensions of the rectangle

Length of the rectangle = (5a + 6b)

Breadth of the rectangle = (5a - 6b)

Step-by-step explanation:

Correct Question

Part A: The area of a square is (9a² - 24a + 16) square units. Determine the length of each side of the square.

Part B: The area of a rectangle is (25a² - 36b²) square units. Determine the dimensions of the rectangle.

Solution

Part A

Area of a square = (side length)²

Area of this square is given as

A = 9a² - 24a + 16

We then factories the given area

A = 9a² - 12a - 12a + 16

A = 3a (3a - 4) - 4 (3a - 4)

A = (3a - 4)(3a - 4)

A = (3a - 4)²

Area of the square = (side length)²

(3a - 4)² = (side length)²

Side length of the square = (3a - 4) units.

Part B

Area of a rectangle = (length) × (breadth)

Area of the rectangle = 25a² - 36b²

25a² - 36b² = (5a + 6b) × (5a - 6b)

Area of a rectangle = (length) × (breadth)

(length) × (breadth) = (5a + 6b) × (5a - 6b)

Length of the rectangle = (5a + 6b)

Breadth of the rectangle = (5a - 6b)

Hope this Helps

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