How many isosceles triangles with integer sides are possible such that the sum of two of the sides is 16 cm?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 24
Let the sides of the triangle be 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 Y can 1, 2, 3,,,,,,,,,,15
In this case total 15 triangles are possible
Case 2, when a + b = 16 (a and b are not equal to 8)
|a - a| < y < a + a
⇒ 0 < b < 2a
⇒ 0 < b < 2(16 - y)
⇒ 0 < b < 32 - 2y
⇒ 0 < 3b < 32
⇒ 0 < b < 10.33
Y can take values from 1 to 10 except 8, so here b can take 9 values
Total number of triangles = 15 + 9
⇒ 24