In an isosceles trapezium, the length of one of the parallel sides, and the lengths of the non-parallel sides are all equal to $30.$ In order to maximize the area of the trapezium, the smallest angle should be:

If the length and breadth of a rectangle are increased by 10% and 70% respectively, the increase in the area of the rectangle will be: 

(A) 87% 

(B) 92% 

(C) 96% 

(D) 95% 

The perimeter of a rectangle is 42 cm. If its diagonal is 15 cm long, find the breadth of the rectangle. 

(A) 8 cm. 

(B) 10 cm. 

(C) 9 cm. 

(D) 7 cm. 

A rectangle with $12 \mathrm{cm}$ and $4 \mathrm{cm}$, reformed into a Rhombus. Both diagonals of Rhombus are equal and one of its angle is ${60}^{\mathrm{o}}$. Find the Area of Newly formed Rhombus.

$5 : 18$ is the ratio of the length and perimeter of a rectangle. What would be the ratio of its length and breadth?