Question
Download Solution PDFIf the sides of a triangle are 7, 12 and x, and x is an integer, then find the number of possible values of x.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Sides of the triangle are 7, 12, and x (where x is an integer).
Formula Used:
For any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
This gives us three inequalities:
1. a + b > c
2. a + c > b
3. b + c > a
Calculation:
Let the sides be 7, 12, and x.
1. 7 + 12 > x
⇒ 19 > x
⇒ x < 19
2. 7 + x > 12
⇒ x > 5
3. 12 + x > 7
⇒ x > -5 (This condition is always true for positive x)
Combining the inequalities:
5 < x < 19
Possible integer values for x are 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18.
Number of possible values of x = 13
The number of possible values of x is 13.
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