(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. ∴
1
2
×5x×12x=270 ⇒x = 3 So, the length of the longest side is13 × 3 = 39 cm.