How many isosceles triangles with integer sides are possible such that the sum of two of the sides is 16 cm?
Answer & explanation
Correct answer: option 4
We know that,
In a triangle,
Sum of two sides is always greater than the third side
Difference of the two sides is always less than the third side
Let the sides of the triangle = a cm, a cm and b cm.
Case 1) when a + a = 16
So, |a - a| < b < a + a
= 0 < b < 2a
= 0 < b < 16
So b can 1, 2, 3,………,15
In this case total 15 triangles are possible
Case 2, when a + b = 16 (x and y are not equal to 8)
|a - a| < b < a + a
= 0 < b < 2a
= 0 < b < 2(16 - b)
= 0 < b < 32 – 2b
= 0 < 3b < 32
= 0 < b < 10.33
b can take values from 1 to 10 except 8, so here y can take 9 values
Total number of triangles = 15 + 9 = 24