Question

Identify an inequality that represents x (in centimeters) for a rectangle with length labeled "x" and width labeled "10 centimeters." The area of the rectangle is greater than or equal to 120 square centimeters.

a) 10+10+x+x≥120
b) 10x≥120
c) 10.10.x.x≥120
d) 10x≤120

Answer 1

The correct inequality for a rectangle with a length 'x' and width '10 centimeters,' having an area of at least 120 square centimeters is '10x ≥ 120,' which is option (b).

Step-by-step explanation:

The question asks us to identify an inequality that represents x (in centimeters) for a rectangle with a length labeled "x" and a width labeled "10 centimeters," given that the area of the rectangle is greater than or equal to 120 square centimeters.

The formula for the area of a rectangle is length × width. So, the inequality representing the area of the rectangle where the length is x and the width is 10 centimeters, would be 10x ≥ 120. This shows that the length (x) times the width (10 cm) should be at least 120 square centimeters.

To find the value of x that satisfies this condition, we can solve the inequality:

1. Multiply x by 10: 10x.
2. Set the inequality: 10x ≥ 120.
3. Divide both sides by 10 to solve for x: x ≥ 12.

Therefore, the correct inequality is option (b) 10x ≥ 120, which represents the lengths in centimeters (x) that will result in an area greater than or equal to 120 square centimeters.