If a and b are the lengths of two sides of a triangle such that the product ab=24

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If a and b are the lengths of two sides of a triangle such that the product ab=24

Try the new Google Books

Check out the new look and enjoy easier access to your favorite features

If a and b are the lengths of two sides of a triangle such that the product ab=24

Try the new Google Books

Check out the new look and enjoy easier access to your favorite features

If a and b are the lengths of two sides of a triangle such that the product ab=24


Page 2

Try the new Google Books

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If a and b are the lengths of two sides of a triangle such that the product ab=24


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.