Assertion: In the given figure, ABCD is a || gm in which DE ⊥ AB and BF ⊥ AD. If AB = 16 cm, DE = 8 cm and BF = 10 cm, then AD is 12 cm.

Reason: Area of a || gm = base × height.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

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Solution

(d) Assertion is false and Reason is true.

Clearly, reason (R) is true.
Assertion: Area of a parallelogram = base × height
$\Rightarrow$ AB × DE = AD × BF
$\Rightarrow$ AD = (16 × 8) ÷ 10 = 12.8 cm
So, the assertion is false.

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(d) Assertion is false and Reason is true. Clearly, reason (R) is true. Assertion: Area of a parallelogram = base × height ⇒AB ×​ DE = AD × BF ⇒AD = (16 × 8) ÷ 10 = 12.8 cm So, the assertion is ​false.

(d) Assertion is false and Reason is true.

Clearly, reason (R) is true.
Assertion: Area of a parallelogram = base × height
$\Rightarrow$ AB × DE = AD × BF
$\Rightarrow$ AD = (16 × 8) ÷ 10 = 12.8 cm
So, the assertion is false.