Question

How many isosceles triangles with integer sides are possible such that sum of two of the side is 12

Answer 1

Step-by-step explanation:

11

When the sum of two equal sides is 12. hence x=6. hence, there will be 11 values of z which are 1 to 11. Hence, the combination of these values will give 11 different triangles.

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Answer 2

Answer :

17

There are 17 isosceles triangles possible with integer sides are possible such that sum of two of the side is 12.

Step by step explanation :

There is the two possibilities : Sum of the 2 equal side are 12 and Sum of the two unequal side is 12.

Lets start with 1st Possibility : Sum of the 2 equal side are 12.

So, If the sum of the two equal side of triangle is 12 then its look a like (A, 6, 6) and the value of A is between 1 to 11.

So, there is 11 Integers exist for the 1st possibility.

2nd Possibility : Sum of the 2 unequal side are 12.

So, integers available for this case :

Possible : (1, 11, 11) , (2, 10, 10) , (3, 9, 9) , (4, 8, 8) , (5, 7, 7) , (5, 5, 7)

Not possible case because the sum of the two smaller digits is less that the larger number, So those are not possible case. { (1, 1, 11) , (2, 2, 10) , (3, 3, 9) , (4, 4, 8) }

So, there is 6 Integers exist for the 2nd possibility.

So,

There are 17 (11 + 6) isosceles triangles possible with integer sides are possible such that sum of two of the side is 12.

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