The sides of a scalene acute triangle are 14 , 22 , and x. x is intrger and 22 is the largest side of a triangle,what will be the avg manimum and maximum value of x.
Answers
hey mate your answer
'a', 'b', and 'l' are the 3 sides of an acute triangle where 'l' is the longest side then l2 < a2 + b2
The sides are 10, 12, and 'x'.
Scenario 1: Among the 3 sides 10, 12, and x, for values of x ≤ 12, 12 is the longest side.
Scenario 2: For values of x > 12, x is the longest side
Possibilities in scenario 1:
When x ≤ 12, let us find the number of values for x that will satisfy the inequality 122 < 102 + x2
i.e., 144 < 100 + x2
The least integer value of x that satisfies this inequality is 7.
The inequality will hold true for x = 7, 8, 9, 10, 11, and 12. i.e., 6 values.
Possibilities in scenario 2:
When x > 12, x is the longest side.
Let us count the number of values of x that will satisfy the inequality x2 < 102 + 122
i.e., x2 < 244
x = 13, 14, and 15 satisfy the inequality. That is 3 more values.
Hence, the values of x for which 10, 12, and x will form sides of an acute triangle are x = 7, 8, 9, 10, 11, 12, 13, 14, 15. A total of 9 values.