Question

Aisha reduced the size of her square driveway. She made one side 10 feet shorter and the other side 15 feet shorter. The smaller rectangular driveway will have an area of no more than 800 square feet.

Use the drop-down menus to write an inequality to model this situation

Answer 1

Answer: (x - 10)(x - 15) ≤ 800

Explanation:

o represent this situation with an inequality, we can start by considering the original size of Aisha's square driveway. Let's call the original side length of the square "x" feet.

When Aisha reduces one side by 10 feet, the new length becomes (x - 10) feet, and when she reduces the other side by 15 feet, the new width becomes (x - 15) feet.

The area of the smaller rectangular driveway will be the product of these two dimensions, and it should be no more than 800 square feet. So the inequality would be:

(x - 10)(x - 15) ≤ 800

This inequality represents the condition that the area of the smaller rectangular driveway (after reducing the sides of the square) should be less than or equal to 800 square feet.

Answer 2

To model the situation described, we can use an inequality to represent the area of the smaller rectangular driveway.

Let's assume the original side lengths of the square driveway were "s". Aisha reduced one side by 10 feet, so the new length is "s - 10". Similarly, she reduced the other side by 15 feet, so the new width is "s - 15".

The area of a rectangle is calculated by multiplying the length and width. Therefore, the area of the smaller rectangular driveway is:

Area = (s - 10)(s - 15)

The problem states that the area of the smaller driveway should be no more than 800 square feet. We can represent this as an inequality:

(s - 10)(s - 15) ≤ 800

So, the inequality that models the situation is: (s - 10)(s - 15) ≤ 800.

Please note that this inequality assumes that the dimensions of the driveway cannot be negative.