Question

3.5x + 2 m
0.5x m
the expression that models the area of the rectangle is
select...
square meters.
using the distributive property, you can write the simplified expression
select...
square meters.
if the value of x = 3, the area of the rectangle is
square meters.

Explanation:

Step1: Write the area formula

The area of a rectangle is \(A = \text{length}\times\text{width}\). Here, length \(l=3.5x + 2\) and width \(w = 0.5x\). So the area \(A=(3.5x + 2)\times0.5x\).

Step2: Use the distributive property

$$
LATEXBLOCK0
$$

Step3: Substitute \(x = 3\) into the simplified formula

When \(x = 3\), \(A=1.75\times3^{2}+3\). First, calculate \(3^{2}=9\). Then \(1.75\times9 = 15.75\). So \(A=15.75+3=18.75\).

Answer:

The expression that models the area of the rectangle is \((3.5x + 2)\times0.5x\) square meters. Using the distributive property, you can write the simplified expression \(1.75x^{2}+x\) square meters. If the value of \(x = 3\), the area of the rectangle is \(18.75\) square meters.