Question

Juanita designed a vegetable garden in the shape of a square and purchased fencing for that design. then she decided to change that design to a rectangle.

a. the square garden had an area of x^2 ft^2. the area pf the rectangular garden is (x^2-25) ft^2. factor this expression.
b. the rectangular garden must have the same perimeter as the square garden, so jaunita added a number of feet to the length and subtracted the same number of feet from the width. use your factors from part a to determine how many feet were added to the length and subtracted from the width
c. if the original length

Answer 1

To factor the expression (x^2 - 25) ft^2, use the difference of squares formula and factor it as (x + 5) (x - 5) ft^2. The additional feet added to the length and subtracted from the width of the rectangular garden are both 5 ft. If the original length of the square garden is x ft, the final length of the rectangular garden is (x + 5) ft.

Step-by-step explanation:

a. To factor the expression (x^2 - 25) ft^2, we can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b). In this case, a = x and b = 5. So, the expression can be factored as (x + 5)(x - 5) ft^2.

b. Since the rectangular garden must have the same perimeter as the square garden, we can use the factored expression from part a to determine how many feet were added to the length and subtracted from the width. Since the length is represented by (x + 5) ft and the width is represented by (x - 5) ft, the additional feet added to the length and subtracted from the width are both 5 ft.

c. The original length of the square garden is x ft. Since Juanita added 5 ft to the length when she changed the design to a rectangle, the final length of the rectangular garden is (x + 5) ft.

Answer 2

The answer to this question is B.