Question
2) A room is twice as long as it is wide. It has an area of 200m Find its width
Answers
GPT-4o mini
Let's denote the width of the room as \( w \) meters. Since the room is twice as long as it is wide, we can express the length \( l \) of the room as:
\[
l = 2w
\]
The area \( A \) of a rectangle is given by the formula:
\[
A = l \times w
\]
In this case, we know the area is 200 m², so we can set up the equation:
\[
200 = (2w) \times w
\]
This simplifies to:
\[
200 = 2w^2
\]
Now, divide both sides by 2:
\[
100 = w^2
\]
Next, take the square root of both sides:
\[
w = \sqrt{100} = 10
\]
Thus, the width of the room is:
\[
\boxed{10 \text{ m}}
\]
\[
l = 2w
\]
The area \( A \) of a rectangle is given by the formula:
\[
A = l \times w
\]
In this case, we know the area is 200 m², so we can set up the equation:
\[
200 = (2w) \times w
\]
This simplifies to:
\[
200 = 2w^2
\]
Now, divide both sides by 2:
\[
100 = w^2
\]
Next, take the square root of both sides:
\[
w = \sqrt{100} = 10
\]
Thus, the width of the room is:
\[
\boxed{10 \text{ m}}
\]