Question

if abcd is a rectangle, then ae is equal to (a) 80 units (c) 85 units (b) 90 units (d) 70 units​

Answer 1

Given :- ABCD is a rectangle .

To Find :- AE = ?

(a) 80 units (c) 85 units (b) 90 units (d) 70 units

Solution :-

since ABCD is a rectangle, we have,

→ DA = CB { Opposite sides of rectangle are equal in measure .}

→ DA = 40 units

→ ∠ADC = 90° { Each angle of a rectangle is equal to 90° }

→ ∠ADE = 90°

now, in right angled ∆ADE we have,

→ ∠DAE = 60° { given }

So,

→ cos 60° = DA/AE

→ 1/2 = 40/AE

→ AE = 40 × 2

→ AE = 80 units (a) (Ans.)

Hence, length of AE is equal to 80 units .

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Answer 2

Answer: 80 units

Step by step explanation:

AD=BC

AD=40 units

We need to find AE

It is the hypotenuse of ∆ADE

To find AE,

cos A= a/h

cos60°= 1/2

1/2=40/h

h=40×2

h= 40 units

Hence proved