If two rectangles have equal area, then they are congruent.

True

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False

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Solution

The correct option is B False
The given statement is false.
Reason: Area of a rectangle $=$ length $\times$ breadth
Two rectangles can have the same area. However, the lengths of their sides can vary and hence they are not congruent.
Example: Suppose rectangle $1$ has sides $8 m$ and $8 m$ and area equal to $64 m^{2}$ .
Rectangle $2$ has sides $16 m$ and $4 m$ and area $64 m^{2}$ .
Then rectangle $1$ and $2$ are not congruent.
So, $B$ is the correct option.

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Similar questions

Q. Which of the following statements are true and which are false;
(i) All squares are congruent.
(ii) If two squares have equal areas, they are congruent.
(iii) If two rectangles have equal area, they are congruent.
(iv) If two triangles are equal in area, they are congruent.

Q. Fill in the blanks:

(i) Two lines segments are congruent if they have ...... .
(ii) Two angles are congruent if they have ...... .
(iii) Two squares are congruent if they have ...... .
(iv) Two circles are congruent if they have ...... .
(v) Two rectangles are congruent if they have ...... .
(vi) Two triangles are congruent if they have ...... .

Statement 1: If two figures A and B are congruent, then they must have equal area.

Statement 2: If two figures A and B have equal area, then they must be congruent.

Q. If two squares have equal area, they are congruent.

Consider the following two statements:
Statement - 1: If two figures have same shape and same size then they are called congruent.
Statement - 2: If two figures have equal area they are called congruent.
Now, choose the correct option.

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