#
29. In the adjoining figure, ABCD is a rectangle. Its diagonal AC = 15 cm and $\angle $ACD = $\alpha $. If cot $\alpha =\frac{3}{2}$ , find the perimeter and area of the rectangle.

30. Using the measurements given in figure alongside,

(a) find the values of :

(1) sin $\varphi $ (ii) tan $\theta $.

(b) write an expression for AD in terms of $\theta $.

Hint: (b) CD = 5. Draw DE perpendicular to AB, BE = 5, EA = 9.