Rectangle Dimensions Using Linear Equations

 

❓ Question

Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.

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🖼️ Solution Image

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✍️ Short Concept

This question is based on:

👉 Pair of Linear Equations / Linear Equation in One Variable

👉 Perimeter of a Rectangle

👉 Forming Equations from Word Problems

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🔷 Step 1 — Assume Variables

Let the width of the garden be

$$x \text{ m}$$

Since length is 4 m more than width,

$$\text{Length}=x+4 \text{ m}$$

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🔷 Step 2 — Use Given Condition

Perimeter of a rectangle:

$$P=2(l+b)$$

Half perimeter is given as 36 m.

Therefore,

$$l+b=36$$

Substituting values:

$$(x+4)+x=36$$
$$2x+4=36$$

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🔷 Step 3 — Solve the Equation

$$2x=32$$
$$x=16$$

So,

$$\text{Width}=16\text{ m}$$

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🔷 Step 4 — Find Length

$$\text{Length}=x+4$$
$$=16+4$$
$$=20\text{ m}$$

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✅ Final Answer

$$\boxed{\text{Width}=16\text{ m}}$$
$$\boxed{\text{Length}=20\text{ m}}$$

Hence, the dimensions of the garden are:

$$\boxed{20\text{ m}\times16\text{ m}}$$

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🚨 Common Mistakes

❌ Using half perimeter as $2(l+b)$

❌ Taking length as $x-4$

❌ Forgetting to substitute the value of width back to find length

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✅ Final Takeaway

For rectangle problems:

$$\text{Half Perimeter}=l+b$$

Always:

✔ Assume one dimension as a variable

✔ Express the other dimension using the given condition

✔ Form an equation and solve

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📚 Related Topics

• Find Zeroes and Verify Relationship Between Coefficients
• Find Quadratic Polynomial from Sum and Product of Zeroes
• Quadratic Polynomial with Irrational Zeroes Explained