The area of trapezium is $$540{ cm }^{ 2 }$$. If the ratio of parallel sides is $$7:5$$ and the distance between them is $$18cm$$, find the lengths of parallel sides.
Let's assume the two parallel sides of trapezium to be $$7x$$ and $$5x$$
Given, Height of trapezium $$=18cm$$
Now,
Area of trapezium $$=\cfrac { 1 }{ 2 } \times $$ Sum of parallel sides $$\times$$ height
$$\Rightarrow 540=\cfrac { 1 }{ 2 } \times (7x+5x)\times 18$$
$$\Rightarrow 540=\cfrac { 1 }{ 2 } \times 12x\times 18$$
$$\Rightarrow 540=108x$$
$$\Rightarrow x=\dfrac{540}{108}$$
$$\Rightarrow x=5 \ cm$$
Hence the two parallel sides are
$$7x=7\times 5=35cm$$ and $$5x=5\times 5=25cm$$