Page 2Page 2Concept: The length of the third side of a triangle must always be between (but not equal to) the sum and the difference of the other two sides. Let a, b and c are the sides of a triangle, where (a - b) < c < (a + b). Given: Product of two sides a and b = 24 Calculation: It is given that ab = 24, we can have different possible values of a and b such that: ⇒ 1 × 24 :- (24 - 1) < c < ( 24 + 1), c = 24 ⇒ 2 × 12 :- (12 - 2) < c < ( 12 + 2), c = 11, 12, 13 ⇒ 3 × 8 :- (8 - 3) < c < ( 8 + 3), c = 6, 7, 8, 9, 10 ⇒ 4 × 6 :- (6 - 4) < c < ( 6 + 4), c = 3, 4, 5, 6, 7, 8, 9 By studying the given conditions, the third side, c can take 16 different values. ∴ The number of triangles possible for ab = 24 is 16. |