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half the perimeter of a rectangular garden,whose length is 4m more than its width 36m.Find the dimensions of the garden.
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Problem:
The problem states that the length of a rectangular garden is 4m more than its width. The perimeter of the garden is 36m. We need to find the dimensions of the garden.
Solution:
Let's assume the width of the garden is x meters. Since the length is 4m more than the width, we can say that the length of the garden is (x + 4) meters.
Perimeter of a Rectangle:
The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
In this case, the perimeter is given as 36m. So, we can write the equation as:
36 = 2[(x + 4) + x]
Simplifying the Equation:
Let's simplify the equation step by step.
1. Distribute 2 to both terms inside the brackets:
36 = 2x + 8 + 2x
2. Combine like terms:
36 = 4x + 8
3. Subtract 8 from both sides of the equation:
36 - 8 = 4x
28 = 4x
4. Divide both sides of the equation by 4:
28/4 = x
7 = x
Calculating the Length:
Now that we have the value of x, which is the width of the garden, we can substitute it back into the equation to find the length.
Length = x + 4
Length = 7 + 4
Length = 11
Dimensions of the Garden:
Therefore, the width of the garden is 7m and the length of the garden is 11m.
Verification:
To verify our solution, we can calculate the perimeter of the garden using the obtained dimensions.
Perimeter = 2(Length + Width)
Perimeter = 2(11 + 7)
Perimeter = 2(18)
Perimeter = 36
The perimeter of the garden is indeed 36m, which confirms that our solution is correct.
The problem states that the length of a rectangular garden is 4m more than its width. The perimeter of the garden is 36m. We need to find the dimensions of the garden.
Solution:
Let's assume the width of the garden is x meters. Since the length is 4m more than the width, we can say that the length of the garden is (x + 4) meters.
Perimeter of a Rectangle:
The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
In this case, the perimeter is given as 36m. So, we can write the equation as:
36 = 2[(x + 4) + x]
Simplifying the Equation:
Let's simplify the equation step by step.
1. Distribute 2 to both terms inside the brackets:
36 = 2x + 8 + 2x
2. Combine like terms:
36 = 4x + 8
3. Subtract 8 from both sides of the equation:
36 - 8 = 4x
28 = 4x
4. Divide both sides of the equation by 4:
28/4 = x
7 = x
Calculating the Length:
Now that we have the value of x, which is the width of the garden, we can substitute it back into the equation to find the length.
Length = x + 4
Length = 7 + 4
Length = 11
Dimensions of the Garden:
Therefore, the width of the garden is 7m and the length of the garden is 11m.
Verification:
To verify our solution, we can calculate the perimeter of the garden using the obtained dimensions.
Perimeter = 2(Length + Width)
Perimeter = 2(11 + 7)
Perimeter = 2(18)
Perimeter = 36
The perimeter of the garden is indeed 36m, which confirms that our solution is correct.
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half the perimeter of a rectangular garden,whose length is 4m more than its width 36m.Find the dimensions of the garden. Related: Facts That Matter,Pair of Linear Equations in TwoVariables - Mathematics for Class 10th
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