Question 12

The sides of triangle are 3 consecutive even integers with the largest side being less than 13. What is the total number of such triangles?

Solution

We have 4 cases
1: Largest side = 12 then Sides of the triangle are 8,10,12
2: Largest side = 10 then Sides of the triangle are 10,8,6
3: Largest side = 8 then Sides of the triangle are 8,6,4
4: Largest side = 6 then Sides of the triangle are 6,4,2
According to the properties of the triangle,
Sum of any two sides of a triangle is greater than the third side and difference of any two sides of a triangle is lesser than the third side
All the above cases satisfy the properties of the triangle except case 4
Hence C is the correct answer.

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