Question

# Find the number of acute triangles that can be formed with two of its sides equal to 8 and 15.2345

Solution

## The correct option is C 4For 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>82⇒x2>225−64  ⇒64+225>x2  x2+152>82⇒x2>161  ⇒289>x2  ∴x>0Since x=integer∴x=0,1,2,3∴x=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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