Out of two figures if one has larger area, then its perimeter need not to be larger than the other figure. Is the given statement true or false?

Solution:

Given, out of two figures if one has a larger area, then its perimeter need not to be larger than the other figure.

We have to determine if the given statement is true or false.

Area is the amount of space occupied by a two-dimensional figure.

Perimeter is the total length of the boundary of any closed shape.

Let us consider two figures a square and a rectangle,

(i) square with side 6 cm

Area of square = (side)²

= (6)²

= 36 cm²

Perimeter of square = 4(side)

= 4(6)

= 24 cm

(ii) a rectangle with length 5 cm and breadth 2 cm

Area of rectangle = length × breadth

= 5(2)

= 10 cm²

Perimeter = 2(length + breadth)

= 2(5 + 2)

= 2(7)

= 14 cm

We observe that the area of the square is larger than the area of the rectangle, but the perimeter is not larger than the rectangles.

Therefore, the given statement is true.

✦ Try This: Out of two figures if one has a larger area, then its perimeter will be equal. State whether the statement is true or false.

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 11

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NCERT Exemplar Class 7 Maths Chapter 9 Problem 72

Out of two figures if one has larger area, then its perimeter need not to be larger than the other figure. Is the given statement true or false?

Summary:

The given statement, “Out of two figures if one has a larger area, then its perimeter need not to be larger than the other figure” is true.

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