Area of square is 64 sq.cm. perimeter of rectangle is equal to the perimeter of the square find the lenth of the rectangle if its bredth is 6.5 cm which figure has greater area ?
Answers
Question:
Area of square is 64 cm². Perimeter of rectangle is equal to the perimeter of the square. Find the lenth of the rectangle if its bredth is 6.5 cm which figure has greater area ?
Answer:
- The length of the rectangle is 9.5 cm.
- The square has greater area than the rectangle.
Given:
- The area of the square is 64 cm².
- The perimeter of the square is equal to the area of the rectangle.
- The breadth of the rectangle is 6.5 cm.
To find:
- The length of the rectangle.
- The figure which has greater area.
Explanation:
The area of the square is 64 cm².
∴ The length of the side of the square = √(64)
= 8 cm.
∴ The perimeter of the square_
(4×side)
= (4×8) cm
= 32 cm.
We know that,
The perimeter of the square = The perimeter of the rectangle = 32 cm
∴ The perieter of the rectangle is 32 cm.
The breadth of the rectangle is 6.5 cm.
Perimeter = 2×(Length + Breadth)
⇒ 32 = 2×(Length+6.5)
⇒(32/2) = (Length+6.5)
⇒ Length = 16.0-6.5
⇒ Length = 9.5 cm
∴ The length of the rectangle is 9.5 cm.
∴ The area of the rectangle_
(Length × Breadth)
= (9.5×6.5) cm²
= 61.75 cm².
Hence,
64 cm²> 61.75 cm².
∴ The area of the square is greater than the area of the rectangle.