SOLUTION: The length of the longest side is the integer given. What value(s) of x make the triangle? x-4 , x+7, 45 ; Acute triangle

Question 1191818: The length of the longest side is the integer given. What value(s) of x make the triangle? x-4 , x+7, 45 ; Acute triangle
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

Finding the maximum possible value of x is easy. It is given that the longest side is 45, so

To determine the smallest possible values of x, note that the triangle is a right triangle if

So the triangle is acute if

Use the quadratic formula to find

= 29.805 to 3 decimal places

So the triangle with longest side 45 and the other two sides x-4 and x+7 is acute for any value greater than (approximately) 29.805 and less than 38.

ANSWER: 29.805 < x < 38

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