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Congruence — MATHS STD 7 — Question

Gujarat BoardEnglish MediumSTD 7MATHSCongruence1 Mark
MCQ
Assertion (A): If two squares have equal areas, they are congruent.
Reason (R): If two rectangles have equal areas, they are congruent.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
  • B
    Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
  • ✓
    Assertion (A) is true but Reason (R) is false.
  • D
    Assertion (A) is false but Reason (R) is true.
✓

Answer

Correct option: C.
Assertion (A) is true but Reason (R) is false.
(c): Area of a square with sides of length ' $a$ ' is $a^2$.
So, if two squares have equal areas then they have equal side length and therefore they are congruent.
$\therefore A$ is true.
Consider two rectangles one having $l=10 cm, b=2 cm$ and the other having $l=5 cm$, $b=4 cm$.
Both rectangles have the same area of $20 cm^2$ but they are not congruent since they do not have the same length and breadth. $\therefore R$ is false.

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