The longest side of a triangle is 40 cm. Another side of the triangle is 20 cm. The area of the triangle is 320 cm2. Find the length of the third side.

Let the other side be 2a (to simplify calculations) . Hence we have s = (40 + 20 + 2a) / 2 = 30 + a
Hence area = $$\sqrt{(30 + a )(30 + a - 40 )(30 + a - 20)(30 + a - 2a)}$$
= $$\sqrt{(30 + a )( a - 10 )(a + 10 )(30 - a)}$$
= $$\sqrt{(900 - a^2 )( a^2 - 100 )}$$
Hence we have $$\sqrt{(900 - a^2 )( a^2 - 100 )} = 320$$
=> $$(900 - a^2 )( a^2 - 100 ) = 102400$$
Solving we get $$a^2 = 260, 740$$
=> the other side can be $$2\sqrt{260}$$ or $$2\sqrt{740}$$
The other side can't be $$2\sqrt{740}$$, since it is greater than the longest side of 40 cm. Hence the other side is $$2\sqrt{260}$$