To solve this problem, we need to find the breadth of a rectangular piece given the total length of the rod and the ratio of the length to the breadth. Here are the steps to arrive at the solution:
1. Understanding the problem:
- The total length of the rod is 44 meters.
- The ratio of the length (L) to the breadth (B) of the rectangle is 7:4.
2. Expressing length and breadth in terms of a common variable:
- Let the length of the rectangle be [tex]\( 7x \)[/tex] and the breadth of the rectangle be [tex]\( 4x \)[/tex].
3. Setting up the perimeter equation:
- The perimeter of a rectangle [tex]\( P \)[/tex] is given by [tex]\( 2(L + B) \)[/tex].
- Substituting the values we get:
[tex]\[
P = 2(7x + 4x)
\][/tex]
- Since the total remaining length of the rod equals the perimeter of the rectangle, we have:
[tex]\[
2(7x + 4x) = 44
\][/tex]
4. Simplifying the equation:
- Combine the terms inside the parentheses:
[tex]\[
2(11x) = 44
\][/tex]
- This simplifies to:
[tex]\[
22x = 44
\][/tex]
5. Solving for [tex]\( x \)[/tex]:
- Divide both sides by 22:
[tex]\[
x = \frac{44}{22}
\][/tex]
[tex]\[
x = 2
\][/tex]
6. Finding the breadth:
- Substitute the value of [tex]\( x \)[/tex] back into the expression for the breadth:
[tex]\[
B = 4x
\][/tex]
[tex]\[
B = 4 \times 2
\][/tex]
[tex]\[
B = 8 \text{ meters}
\][/tex]
Hence, the breadth of the rectangular shape is 8 meters.
So, the correct answer is:
A. 8 m
