Question

The area of a rectangle, R, is no less than 8 square meters. The area of a triangle, T, is more than one-half the area of the rectangle. Which system of inequalities models this situation?

Answer 1

The system of inequalities for the areas of a rectangle R and a triangle T, given that R is no less than 8 square meters and T is more than half R's area, is expressed as R ≥ 8 for the rectangle, and T > R/2 for the triangle, which can also be simplified to T > 4.

Step-by-step explanation:

The situation described deals with two geometric figures and compares their areas, which means the question falls under the area of Mathematics. To create an inequality system that models the situation, we need two inequalities. For the rectangle, R, with an area no less than 8 square meters, we write the inequality R ≥ 8. For the triangle, T, with an area more than half of the rectangle's area, we write T > R/2. Therefore, the system of inequalities is:

• R ≥ 8 (Area of rectangle)
• T > R/2 (Area of triangle)

Note that to be more precise in the second inequality, we can substitute R with ≥ 8, yielding T > 8/2, which simplifies to T > 4.