If x and y are the lengths of two sides of a triangle such that the product xy=18, where x and y are

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03 Jun 2022 Geometry

If x and y are the lengths of two sides of a triangle such that the product xy=18, where x and y are integers, then how many such triangles are possible ?

OPtion

1) 7
2) 10
3) 4
4) 9
5) 5
6) 12
7) 8
8) 6
9) 13
10) None of these

Solution

The length of third side of a triangle must always be between 'Sum and the difference of other two sides '
Let x, y and z are sides of a triangle, where (x-y) < z < (x+y)
Given, product of two sides x and y = xy = 18
Different possible values of (x,y) are (1,18) (2,9) (3,6)
For x=1, y=18 : (18-1) < z < (18+1), z=18
For x=2, y=9 : (9-2) < z < (9+2), z=8, 9, 10
For x=3, y=6 : (6-3) < z < (6+3), z=4, 5, 6, 7, 8
Thus third side z can take 9 different values.
Correct Option 4)

Correct Option: 4 Best Solution (0)