Question

In a rectangle ABCD, it's diagonal AC=15cm and angle ACD = alpha. if cot alpha=3/2, find perimeter and area of the rectangle.​

Answer 1

Answer:

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