Q12------------------How many isosceles triangles?

Question

Q12------------------How many isosceles triangles can be formed having integral sides ,such that perimeter is 22.
a. 10
b. 9
c. 8
d. 5

Answer 1

Let the equal sides be of length x and the third side be of length y.

Also,
2x + y = 22
y = 22 - 2x

We get two conditions:
1) y is even.
2) According to triangle inequalities, 2x > y

So, using the conditions, y can assume any even integral value less than 11.

y = 2, 4, 6, 8, 10.

Total 5 isosceles triangles can be formed having integral sides and perimeter of 22.

Answer 2

::

If the sides are x, x, and y

2x + y = 22

Since the sides are integers then y must be an even number from 2 to 20, and there are 10 such numbers. Answer is a. 10.

Answer 3

since triangle is isoceles, its sides would be x,x, y

now x+x+y = 2x+y = 22

value of y can be between (0-22) and should be integer
since x = (22-y)/2 should be integer too, y has to be even number.
0 and 22 are excluded as it reduces to point and not triangle.
only possible values left are 2,4,6,8,10,12,14,16,18,20
ie 10
so a is correct

Answer 4

The constraint that all sides must be integers requires that the sum of the two equal sides must be an even number< = 20. There are ten such.
So, 10 is the answer.

Answer 5

C. 8