Question

Faye says that the perimeter of the rectangle shown is 2x + (x + 10) + 2x + (x + 10) Khai says that the perimeter is 2(2x) + 2(x + 10) Jesse says that the perimeter is 4x + 20. who's correct and explain

Answer 1

To determine who is correct regarding the perimeter of the rectangle, let's break down the information given by each person.

1. **Faye's Calculation**:
Faye stated the perimeter as:
\[
P = 2x + (x + 10) + 2x + (x + 10)
\]
We can combine like terms:
- First, simplify the terms:
\[
P = (2x + 2x) + (x + 10 + x + 10) = 4x + 2x + 20 = 4x + 20
\]

2. **Khai's Calculation**:
Khai stated the perimeter as:
\[
P = 2(2x) + 2(x + 10)
\]
Let's simplify this:
- First, distribute the factors:
\[
P = 4x + 2(x + 10) = 4x + 2x + 20 = 6x + 20
\]

3. **Jesse's Calculation**:
Jesse stated the perimeter as:
\[
P = 4x + 20
\]

Now, we can compare the results:
- **Faye**: \(P = 4x + 20\)
- **Khai**: \(P = 6x + 20\)
- **Jesse**: \(P = 4x + 20\)

**Conclusion**:
Faye and Jesse both calculated the perimeter as \(4x + 20\), which is correct. Khai's calculation, \(6x + 20\), is incorrect.

The correct perimeter of the rectangle is indeed \(4x + 20\). Thus, Faye and Jesse are correct.