Question

in the adjoining figure abcd is a rectangle .its diagonal AC =15 cm and angle ACD =a .if cot a =3/2 , find the perimeter and area of the rectangle .<br />plz someone answer very urgent .

Answer 1

The perimeter is 150/√13.

Step-by-step explanation:

Let's say if theta is the angle between diagonal and the side of the rectangle then

AB/BC = cot θ

If cotθ = 3/2 then sinθ = 2/√13

Sin θ = BC/AC

2/√13 = BC / 15

BC = 30/ √ 13

Similarly cos θ  = 3/√13

cos θ  = AB/AC =AB/15

3/√ 15 =AB /15 so AB = 45/√13

So perimeter = 2(AB+ BC)

                       = 2(30/√ 13  + 45/√ 13)

                      = 150/√13

Hence the perimeter is 150/√13.

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Answer 2

Answer:

Step-by-step explanation:

theta is the angle between diagonal and the side of the rectangle then

AB/BC = cotø

if cotø = 3/2 then sinø = 2/underoot 13

and sin ø = BC/AC

2/underoot 13 = BC / 15

so BC = 30/ underoot 13

similarly cos ø = 3/underoot 13

and cos ø = AB/AC =AB/15

3/underoot 15 =AB /15 so AB = 45/underoot 13

So perimeter = 2(AB+ BC)

= 2(30/underoot 13 + 45/underoot 13)

= 150/underoot13