A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?
Solution:
The perimeter of the rectangular field and square area same.
It is given that the perimeter of the square and the rectangular field is the same, so we can find the breadth of the rectangular field followed by the area of the rectangular field.
Side of the square = 60m
Length of the rectangle = 80m
Perimeter of the square = 4 × (side of square) = 4 × 60m = 240m
Perimeter of rectangle = 2 × (length + breadth)
Perimeter of square = Perimeter of rectangle
240 = 2 (length + breadth)
240 = 2 (80 + breadth)
240 = 160 + 2 × breadth
240 - 160 = 2 × breadth
80 = 2 × breadth
breadth = 80/2 = 40 m
Area of the square = side × side = 60 × 60 = 3600 m2
Area of the rectangular field = length × breadth = 80 × 40 = 3200 m2
Thus, area of square is larger than the area of rectangular field.
☛ Check: NCERT Solutions for Class 8 Maths Chapter 11
Video Solution:
A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?
Class 8 Maths NCERT Solutions Chapter 11 Exercise 11.1 Question 1
Summary:
A square and a rectangular field with measurements as given in the figure have the same perimeter. The area of the square is larger than the area of the rectangular field.
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