Try the new Google Books
Check out the new look and enjoy easier access to your favorite features
Try the new Google Books
Check out the new look and enjoy easier access to your favorite features
Try the new Google Books
Check out the new look and enjoy easier access to your favorite features
Page 2
Try the new Google Books
Check out the new look and enjoy easier access to your favorite features
Page 2
Concept:
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.