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Question

Find the number of acute triangles that can be formed with two of its sides equal to 8 and 15.
  1. 2
  2. 3
  3. 4
  4. 5


Solution

The correct option is C 4
For an acute Δ, we have condition;
a2+b2>c2 [where a,b,c are the sides of acute Δ]
Another condition that we'll use is the sum of 2 sides in a triangle is greater than the third side. So, let the third side be x.
Applying the first condition we get;
82+x2>152  82+152>x2  x2+152>82x2>22564  64+225>x2  x2+152>82x2>161  289>x2  x>0Since x=integerx=0,1,2,3x=13,14,15,16,17    4,5,6,7,8     9,10,11,12     13,14,15,16 
          I
Applying the second condition, we get
8+x>15  8+15>x  x+15>8x>7x<23x>7
          II
Combining the two conditions from 1 and II we get
X = 13, 14, 15, 16
The answer is 4.

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