SSC CPO SI and ASI Model Paper 4

(3) The sides of a triangle are 5x,12x and 13x.
Here (13x)2 = (5x)2 + (12x)2 [Thelength of the largest side is equal tothe square root of the sum of thesquares of other two sides in a rightangled triangle.]
Thus, the given triangle is a rightangled triangle.
$\therefore \frac{1}{2}\times 5\mathit{x}\times 12\mathit{x}=270$
⇒x = 3
So, the length of the longest side is13 × 3 = 39 cm.