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A Square and a Rectangular Field with Measurements as Given in the Figure Have the Same Perimeter. Which Field Has a Larger Area? - Mathematics

A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?

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Solution

Perimeter of square = 4 (Side of the square) = 4 (60 m) = 240 m

Perimeter of rectangle = 2 (Length + Breadth)

= 2 (80 m + Breadth)

= 160 m + 2 × Breadth

It is given that the perimeter of the square and the rectangle are the same.

160 m + 2 × Breadth = 240 m

Breadth of the rectangle  = `(80/2)m `= 40 m

Area of square = (Side)2 = (60 m)2 = 3600 m2

Area of rectangle = Length × Breadth = (80 × 40) m2 = 3200 m2

Thus, the area of the square field is larger than the area of the rectangular field.

Concept: Mensuration
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APPEARS IN

NCERT Class 8 Maths Textbook
Chapter 11 Mensuration
Exercise 11.1 | Q 1 | Page 171
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