Mathematics
Assertion (A): If the sides of a rectangular plot are 80 m and 60 m, then the length of its diagonal is 100 m.
Reason (R): In a rectangle, all angles are 90°.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Pythagoras Theorem
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Answer
A rectangle is a quadrilateral with four right angles.
Let ABCD be the rectangular plot.
Thus, in a rectangle, all angles are 90°.
∴ Reason (R) is true.
Given:
Side 1 (AB) = 80 m
Side 2 (BC) = 60 m
Let d be the length of the diagonal (AC). Using pythagoras theorem in triangle ABC,
⇒ AC2 = AB2 + BC2
⇒ d2 = 802 + 602
⇒ d2 = 6400 + 3600
⇒ d2 = 10000
⇒ d =
⇒ d = ± 100 m
Since, length cannot be negative, so, diagonal = 100 m.
∴ Assertion (A) is true.
∴ Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason (or explanation) for Assertion (A).
Hence, option 3 is the correct option.
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