Answer:
Explanation:
Part A: The area of a square is given by the formula A = s^2, where A is the area and s is the length of each side. Since the area of the square in this case is (9a^2 − 24a + 16) square units, we can write the equation 9a^2 − 24a + 16 = s^2. To determine the length of each side of the square, we need to solve for s. We can do this by factoring the left side of the equation completely.
(9a^2 − 24a + 16) can be factored as (3a - 4)^2. Therefore, s = 3a - 4. So, the length of each side of the square is (3a - 4) units.
Part B: The area of a rectangle is given by the formula A = lw, where A is the area, l is the length, and w is the width. Since the area of the rectangle in this case is (25a^2 − 36b^2) square units, we can write the equation 25a^2 − 36b^2 = lw. To determine the dimensions of the rectangle, we need to solve for l and w. We can do this by factoring the left side of the equation completely.
(25a^2 − 36b^2) can be factored as (5a + 6b)(5a - 6b). Therefore, one possible set of dimensions for the rectangle is l = (5a + 6b) and w = (5a - 6b). So, one possible set of dimensions for the rectangle is (5a + 6b) units by (5a - 6b) units.