Question

Assertion (A): ΔABC is equilateral with side 3 cm If AD = 1 cm then EC = 1 cm, ∠ADE = 90°

Reason (R): cos 60° = `(AD)/(AE) = 1/2`

Options

• Both A and R are true, and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

Both A and R are true, and R is the correct reason for A.

Explanation:

From the figure, DE ⊥ AC ⇒ ∠ADE = 90°

From the equilateral ΔABC (side 3 cm), ∠A = 60°.

cos⁡ 60^∘ = `(AD)/(AE) = 1/2`   ...[Using the reason]

AE = 2 cm 

EC = AC − AE 

EC = 3 − 2 

EC = 1 cm