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Length [tex]\([ l ] = 2w \)[/tex]

Garden width [tex]\([ w ] = w \)[/tex]

The perimeter of your rectangular garden is 60 feet.

QUESTION: If the length [tex]\([ l ]\)[/tex] of the garden is twice the width [tex]\([ w ]\)[/tex], what is the length of your garden?

Use the formula for perimeter: [tex]\[ P = 2l + 2w \][/tex]

A. 4 feet
B. 10 feet
C. 20 feet
D. 40 feet

Sagot :

GinnyAnswer
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.
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