Two plots of land have the same perimeter.One is a square of side 64m and the other is a rectangle of length 70m. Find the breadth of the rectangular plot. Which plot has the greater area and by how much?
Answers
Answer:
Plots have same perimeter.
Side of square field = 64m
perimeter = 64*4 = 256m
length of rectangular plot = 70m
breadth = b
2(70+b) = 256
⇒ 70+b = 256/2 = 128
⇒ b = 128 - 70
⇒ b = 58m
Area of square = 64*64 = 4096 m²
Area of rectangle = 70*58 = 4060 m²
Area of square is more than rectangle by = 4096 - 4060 = 36m²
- Length of the square = 64m.
- Length of the rectangle = 70m.
Perimeter of the Square = 4 × Side
Perimeter of the square = 4 × 64
Perimeter of the square = 256 m.
Let breadth of the rectangle = B.
Perimeter of the rectangle = 2(70 +B).
Now, According to question,
2 × (70 + B) = 256
140 + 2B = 256
2B = 256 - 140
2B = 116
Breadth = 58 m.
Area of the rectangle = 58 × 70 = 4,060 sq m.
Area of the square = length × length
Area of the square = 64 × 64 = 4096 sq.m.
Area of the square has more area = 4060 - 4096 = 36 sq.m
- Hence, the square has more area by 36 sq.m.