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Answer :
To determine the value of [tex]\( x \)[/tex] for the given rectangle, let's follow the steps systematically:
1. Identify the given expressions:
- The length of the rectangle is [tex]\( (x + 2) \)[/tex] metres.
- The breadth of the rectangle is [tex]\( (x - 4) \)[/tex] metres.
- The perimeter of the rectangle is given to be 44 metres.
2. Recall the formula for the perimeter of a rectangle:
[tex]\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Breadth})
\][/tex]
3. Substitute the given expressions into the perimeter formula:
[tex]\[
2 \times ((x + 2) + (x - 4)) = 44
\][/tex]
4. Simplify the equation inside the parentheses:
[tex]\[
(x + 2) + (x - 4) = x + x + 2 - 4 = 2x - 2
\][/tex]
5. Substitute [tex]\( 2x - 2 \)[/tex] into the perimeter equation:
[tex]\[
2 \times (2x - 2) = 44
\][/tex]
6. Solve for [tex]\( x \)[/tex]:
- Distribute the 2 on the left side:
[tex]\[
4x - 4 = 44
\][/tex]
- Add 4 to both sides to isolate the [tex]\( 4x \)[/tex] term:
[tex]\[
4x - 4 + 4 = 44 + 4
\][/tex]
[tex]\[
4x = 48
\][/tex]
- Divide both sides by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{48}{4}
\][/tex]
[tex]\[
x = 12
\][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( \boxed{12} \)[/tex].
1. Identify the given expressions:
- The length of the rectangle is [tex]\( (x + 2) \)[/tex] metres.
- The breadth of the rectangle is [tex]\( (x - 4) \)[/tex] metres.
- The perimeter of the rectangle is given to be 44 metres.
2. Recall the formula for the perimeter of a rectangle:
[tex]\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Breadth})
\][/tex]
3. Substitute the given expressions into the perimeter formula:
[tex]\[
2 \times ((x + 2) + (x - 4)) = 44
\][/tex]
4. Simplify the equation inside the parentheses:
[tex]\[
(x + 2) + (x - 4) = x + x + 2 - 4 = 2x - 2
\][/tex]
5. Substitute [tex]\( 2x - 2 \)[/tex] into the perimeter equation:
[tex]\[
2 \times (2x - 2) = 44
\][/tex]
6. Solve for [tex]\( x \)[/tex]:
- Distribute the 2 on the left side:
[tex]\[
4x - 4 = 44
\][/tex]
- Add 4 to both sides to isolate the [tex]\( 4x \)[/tex] term:
[tex]\[
4x - 4 + 4 = 44 + 4
\][/tex]
[tex]\[
4x = 48
\][/tex]
- Divide both sides by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{48}{4}
\][/tex]
[tex]\[
x = 12
\][/tex]
So, the value of [tex]\( x \)[/tex] is [tex]\( \boxed{12} \)[/tex].
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