13.4k views
1 vote
Simon has a certain length of fencing to enclose a rectangular area. The function A models the rectangle's area (in square meters ) as a function of its width (in meters ). area (square meters ) Which of these statements are true? Chnose all answers that annlv:

User CRK
by
8.0k points

1 Answer

0 votes

Answer: all three statements are true

Step-by-step explanation:

The question states that the function A models the rectangle's area as a function of its width. We need to determine which statements are true.

Let's consider the properties of the area of a rectangle in relation to its width:

1. The area of a rectangle is calculated by multiplying its length by its width. Therefore, the function A can be written as A(w) = lw, where w represents the width and l represents the length.

2. The area of a rectangle is always non-negative. This means that the area cannot be negative or zero for any positive value of the width. Therefore, A(w) > 0 for all positive values of w.

3. The area of a rectangle increases as the width increases, assuming the length remains constant. This is because a larger width results in a larger area. Therefore, if we compare two positive values of the width, w1 and w2, where w1 < w2, we have A(w1) < A(w2).

Based on these properties, the true statements are:

- Statement 1: The function A can be written as A(w) = lw, where w represents the width and l represents the length.

- Statement 2: A(w) > 0 for all positive values of w.

- Statement 3: If we compare two positive values of the width, w1 and w2, where w1 < w2, we have A(w1) < A(w2).

Therefore, all three statements are true.

User Helen Hakobyan
by
8.6k points