To solve the problem of finding the dimensions of the rectangular garden, let's work through it step-by-step:
1. Understand the given information:
- Half the perimeter of the rectangle is 36 meters.
- The length [tex]\( l \)[/tex] is 4 meters more than the width [tex]\( w \)[/tex].
2. Express the full perimeter:
- Since half the perimeter is 36 meters, the full perimeter [tex]\(P\)[/tex] is [tex]\( 36 \times 2 = 72 \)[/tex] meters.
3. Use the formula for the perimeter of a rectangle:
- The formula for the perimeter of a rectangle is [tex]\( P = 2(l + w) \)[/tex].
4. Set up the equation using the given information:
- We know that the length [tex]\( l \)[/tex] is 4 meters more than the width [tex]\( w \)[/tex]. Thus, [tex]\( l = w + 4 \)[/tex].
- Substituting this into the perimeter formula, we get [tex]\( P = 2((w + 4) + w) \)[/tex].
5. Simplify the perimeter equation:
- Substitute the full perimeter value (72 meters): [tex]\( 72 = 2(w + 4 + w) \)[/tex].
- Combine like terms inside the parentheses: [tex]\( 72 = 2(2w + 4) \)[/tex].
6. Distribute and solve for [tex]\( w \)[/tex]:
- Distribute the 2: [tex]\( 72 = 4w + 8 \)[/tex].
- Subtract 8 from both sides: [tex]\( 72 - 8 = 4w \)[/tex].
- Simplify: [tex]\( 64 = 4w \)[/tex].
7. Solve for the width [tex]\( w \)[/tex]:
- Divide both sides by 4: [tex]\( w = \frac{64}{4} = 16 \)[/tex].
8. Find the length [tex]\( l \)[/tex]:
- Since [tex]\( l = w + 4 \)[/tex], substitute [tex]\( w = 16 \)[/tex]: [tex]\( l = 16 + 4 = 20 \)[/tex].
Conclusion:
- The width of the rectangular garden is [tex]\( 16 \)[/tex] meters.
- The length of the rectangular garden is [tex]\( 20 \)[/tex] meters.
