The length of a rectangle is 12 cm and its perimeter is 34 cm. What is its breadth?
Answers
Given
- Length of the rectangle = 12cm
- Perimeter of the rectangle = 34cm
⠀
To find
- Breadth of the rectangle.
⠀
Solution
- To find perimeter of a rectangle, we need length and breadth of the rectangle. But in this question, we have length and perimeter of the rectangle.
⠀
Let the breadth of the rectangle be b.
⠀
- We know that
⠀
☆ Perimeter = 2(l + b)
⠀
→ Perimeter = 34
⠀
→ 2(l + b) = 34
⠀
→ 2(12 + b) = 34
⠀
→ 12 + b = 34/2
⠀
→ 12 + b = 17
⠀
→ b = 17 - 12
⠀
→ b = 5cm
⠀
Hence,
- Breadth of the rectangle is 5cm.
⠀
⠀
⠀⠀⠀ ⠀Some Formulae
⠀
→ Area of square = (side)²
⠀
→ Area of rectangle = length × breadth
⠀
→ Area of triangle = ½ × base × height
⠀
→ Area of parallelogram = base × height
⠀
→ Area of Circle = πr²
Given:
- Length of a rectangle = 12cm
- Perimeter of a rectangle = 34cm
⠀
To Find:
- Breadth of the rectangle.
⠀
Understanding:
As we know, to find perimeter of a rectangle, we need length and breadth of the rectangle. But in this question, it is given the perimeter and length of the rectange so here we need to find the breadth:
Required Solution:
Let's assume the breadth of the rectangle as b.
⠀
So,We know that
⠀
Perimeter = 2(length + breadth) or 2(l + b)
⠀
➟ Perimeter = 34cm
⠀
➟ 2(l + b) = 34cm
⠀
➟ 2(12 + b) = 34cm
➟ 12 + b = 34/2 cm
➟ 12 + b = 17cm
⠀
➟ b = 17 - 12cm
➟ b = 5cm
⠀
Therefore,
- Breadth of the rectangle is 5cm.
⠀
___________________________
Verification:
Perimeter = 2(length + breadth) or 2(l + b)
➟ 34cm = 2(12 + 5) cm
➟ 34cm = 2(17)cm
➟ 34cm = 2 × 17cm
➟ 34cm = 34cm
⠀⠀⠀⠀⠀⠀⠀⠀⠀L.H.S = R.H.S