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.

Answer 1

Complete 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. write an inequality to represent the area of the smaller driveway.

Answer:

The inequality that represents the area of the smaller drive way is $x(x-25) \leq 650$

Step-by-step explanation:

Let the original length of the sides of Aisha's square driveway be = x

She made one side 10 ft short, i.e. (x - 10) ft

She made the other side 15 ft short, i.e. (x - 15) ft

Since the sides are no longer equal, the driveway is now a rectangle

The question states that the smaller rectangular driveway will have an area of no more than 800 square feet

Area of a rectangle = length * Breadth

Area = (x - 10)*(x - 15)

$Area = x^{2} - 15x - 10x + 150\\Area = x^{2} - 25x + 150$

Area ≤ 800

$x^{2} - 25x + 150 \leq 800\\ x^{2} - 25x - 650\leq 0\\x(x-25) \leq 650$

Solving the above, x = 40.9 or -15.9

Since the length of a square cannot be negative, x = 40.9 ft

Answer 2

Answer:

(x-10)·(x-15)≤800

Step-by-step explanation:

imagine math