State true or false.

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

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True

False

answer is A.

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Detailed Solution

The given statement is that a square and a rectangular field with measurements as given in the figure have the same perimeter and the field (a) has a larger area.
It is given a figure,
Question Image

Let the side of square field be a = 60 cm
Let the length of the rectangular field is 80 cm and breadth be b cm.
Perimeter of the square is

4 × a

, where ‘a’ is the side.
The area of the square is

a 2

, where ‘a’ is the side.
Perimeter of the rectangle is

2 (l + b)

, where ‘l’ is the length and ‘b’ is the breadth.
The area of the rectangle is

l × b

, where ‘l’ is the length and ‘b’ is the breadth.
According to the given statements,
⇒Perimeter of square = Perimeter of rectangle
⇒ 4 × a = 2(l + b)
⇒4 × 60 = 2(80 + b)
⇒240 = 160 + 2b
⇒2b = 80
⇒b = 40
Area of square is;