Answer :
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
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
