If the areas of two rectangles are same, they are congruent. State whether the statement is true or false.

Solution:

Given, if the areas of two rectangles are same, they are congruent.

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

If two figures have the same shape and the same size, then they are said to be congruent figures.

Area of a rectangle = length × breadth

(i) consider a rectangle with length 6 cm and breadth 2 cm

Area of rectangle = 6 × 2 = 12 square cm

(ii) consider a rectangle with length 4 cm and breadth 3 cm

Area of rectangle = 4 × 3 = 12 square cm

This implies that the rectangles with different length and breadth will also have equal areas.

Two rectangles can be congruent only if they have same length and breadth.

Therefore, the two rectangles of equal areas are not congruent.

✦ Try This: If the length of two rectangles are same, they are congruent. State whether the statement is true or false.

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

NCERT Exemplar Class 7 Maths Chapter 6 Problem 94

Summary:

The given statement,”If the areas of two rectangles are same, they are congruent” is false.

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