find the area of square that has the same perimeter as a rectangle whose length and the breadth are 18 cm and 8 cm.(ans: 169msquare)
Answers
Provided that:
→ Perimeter of rectangle = Perimeter of square
→ Length of rectangle = 18 cm
→ Breadth of rectangle = 8 cm
To calculate:
→ Area of square
Solution:
→ Area of square = 169 cm sq.
Using concepts:
- Perimeter of rectangle formula
- Perimeter of square formula
- Area of square formula
Using formulas:
→ Perimeter of rectangle formula
- 2(l+b)
→ Perimeter of square formula
- 4 × a
→ Area of square formula
- a × a
Where, l denotes length, b denotes breadth and a denotes side.
Required solution:
~ Firstly let us find the perimeter of rectangle!
→ Perimeter = 2(l+b)
→ Perimeter = 2(18+8)
→ Perimeter = 2(26)
→ Perimeter = 52 centimetres
~ Now according to the question,
→ Perimeter of rectangle = Perimeter of square
Henceforth, 52 cm = 52 cm
~ Now let us find out the side of given square by using perimeter of square formula!
→ Perimeter = 4 × a
→ 52 = 4 × a
→ 52/4 = a
→ 13 = a
→ a = 13 cm
→ Side of square = 13 centimetres
~ Now let's calculate area of given square by using suitable formula!
→ Area = a × a
→ Area = 13 × 13
→ Area of square = 169 centimetres sq.