Answer :
To determine the length of the garden, given that the perimeter is 60 feet and the length is twice the width, we can follow these steps:
1. Assign symbols for width and length:
- Let [tex]\( w \)[/tex] represent the width of the garden.
- Since the length is twice the width, let [tex]\( l = 2w \)[/tex].
2. Use the formula for the perimeter of a rectangle:
- The formula for the perimeter of a rectangle is [tex]\( P = 2l + 2w \)[/tex].
3. Substitute the given values and expressions into the formula:
- Given perimeter [tex]\( P = 60 \)[/tex] feet,
- So, [tex]\( 60 = 2(2w) + 2w \)[/tex].
4. Simplify the equation:
- [tex]\( 60 = 4w + 2w \)[/tex].
- [tex]\( 60 = 6w \)[/tex].
5. Solve for width [tex]\( w \)[/tex]:
- [tex]\( w = \frac{60}{6} \)[/tex].
- [tex]\( w = 10 \)[/tex] feet.
6. Calculate the length [tex]\( l \)[/tex]:
- Since [tex]\( l = 2w \)[/tex],
- [tex]\( l = 2 \times 10 \)[/tex].
- [tex]\( l = 20 \)[/tex] feet.
Thus, the length of the garden is 20 feet.
1. Assign symbols for width and length:
- Let [tex]\( w \)[/tex] represent the width of the garden.
- Since the length is twice the width, let [tex]\( l = 2w \)[/tex].
2. Use the formula for the perimeter of a rectangle:
- The formula for the perimeter of a rectangle is [tex]\( P = 2l + 2w \)[/tex].
3. Substitute the given values and expressions into the formula:
- Given perimeter [tex]\( P = 60 \)[/tex] feet,
- So, [tex]\( 60 = 2(2w) + 2w \)[/tex].
4. Simplify the equation:
- [tex]\( 60 = 4w + 2w \)[/tex].
- [tex]\( 60 = 6w \)[/tex].
5. Solve for width [tex]\( w \)[/tex]:
- [tex]\( w = \frac{60}{6} \)[/tex].
- [tex]\( w = 10 \)[/tex] feet.
6. Calculate the length [tex]\( l \)[/tex]:
- Since [tex]\( l = 2w \)[/tex],
- [tex]\( l = 2 \times 10 \)[/tex].
- [tex]\( l = 20 \)[/tex] feet.
Thus, the length of the garden is 20 feet.
