Answer :
To find the width of the rectangle with an area of 120 square meters, given that the length is twice the width, let’s solve it step by step:
1. Define Variables:
- Let [tex]\( w \)[/tex] be the width of the rectangle in meters.
- Since the length is twice the width, the length is [tex]\( 2w \)[/tex] meters.
2. Write the equation for the area:
- The area [tex]\( A \)[/tex] of a rectangle is given by the formula:
[tex]\[
A = \text{length} \times \text{width}
\][/tex]
- Substituting the known values gives us:
[tex]\[
120 = 2w \times w
\][/tex]
- Simplifying the equation:
[tex]\[
120 = 2w^2
\][/tex]
3. Solve for [tex]\( w \)[/tex]:
- Divide both sides by 2 to isolate [tex]\( w^2 \)[/tex]:
[tex]\[
w^2 = 60
\][/tex]
- Take the square root of both sides to find [tex]\( w \)[/tex]:
[tex]\[
w = \sqrt{60}
\][/tex]
- Simplifying [tex]\(\sqrt{60}\)[/tex] gives us approximately 7.75.
4. Choose the correct width from the given options:
- The options are 6 meters, 8 meters, 10 meters, and 12 meters.
- Among these, 8 meters is the nearest whole number to 7.75.
Therefore, the width of the rectangle is 8 meters.
1. Define Variables:
- Let [tex]\( w \)[/tex] be the width of the rectangle in meters.
- Since the length is twice the width, the length is [tex]\( 2w \)[/tex] meters.
2. Write the equation for the area:
- The area [tex]\( A \)[/tex] of a rectangle is given by the formula:
[tex]\[
A = \text{length} \times \text{width}
\][/tex]
- Substituting the known values gives us:
[tex]\[
120 = 2w \times w
\][/tex]
- Simplifying the equation:
[tex]\[
120 = 2w^2
\][/tex]
3. Solve for [tex]\( w \)[/tex]:
- Divide both sides by 2 to isolate [tex]\( w^2 \)[/tex]:
[tex]\[
w^2 = 60
\][/tex]
- Take the square root of both sides to find [tex]\( w \)[/tex]:
[tex]\[
w = \sqrt{60}
\][/tex]
- Simplifying [tex]\(\sqrt{60}\)[/tex] gives us approximately 7.75.
4. Choose the correct width from the given options:
- The options are 6 meters, 8 meters, 10 meters, and 12 meters.
- Among these, 8 meters is the nearest whole number to 7.75.
Therefore, the width of the rectangle is 8 meters.
