for a school assignment, santiago has to give three possibilities for the dimensions of a retangle that has a perimeter of 28 ft and an area greater than 30 ft. what are two other possibilities other than 10ft of base and 4 ft for height

7 by 7

8 by 6

thank u

You're welcome.

To find the three possibilities for the dimensions of a rectangle with a perimeter of 28 ft and an area greater than 30 ft, we can use algebraic equations.

Let's assume the dimensions of the rectangle are the base (B) and height (H).

1. The given condition is that the perimeter is 28 ft:
Perimeter = 2(B + H) = 28 ft

We can solve this equation to find the relation between B and H:
B + H = 14 ft (dividing both sides by 2)

Now, we can express one variable in terms of the other:
B = 14 - H (subtracting H from both sides)

2. The area of the rectangle is greater than 30 ft:
Area = B * H > 30 ft

We can substitute the value of B from the first equation into the second equation:
(14 - H) * H > 30 ft

Simplifying the inequality, we get:
H^2 - 14H + 30 > 0

We can solve this quadratic inequality to find the possible values of H.
By factoring or using the quadratic formula, we get
(H - 5)(H - 9) > 0

This inequality means that H must be greater than 9 or less than 5 for the area to be greater than 30 ft.

Now, let's find the three possible dimensions by substituting values within this range for H and solving for B:

Possibility 1:
If we choose an H value of 10 ft (greater than 9), we can substitute it into the equation B = 14 - H:
B = 14 - 10 = 4 ft
Therefore, one possibility is B = 4 ft and H = 10 ft.

Possibility 2:
If we choose an H value of 4 ft (less than 5), we can substitute it into the equation B = 14 - H:
B = 14 - 4 = 10 ft
Therefore, another possibility is B = 10 ft and H = 4 ft.

Other possibilities can be found by selecting H values within the specified range and repeating the process.

Possibility 3:
For example, we can select H = 6 ft, substitute it into the equation B = 14 - H:
B = 14 - 6 = 8 ft
Therefore, another possibility is B = 8 ft and H = 6 ft.

So, the three possibilities for the dimensions of the rectangle are:
1. B = 4 ft, H = 10 ft
2. B = 10 ft, H = 4 ft
3. B = 8 ft, H = 6 ft