Question

The length of 2 sides of a triangle 5 centimetres and 7 cm. If the third side is an integer , what is the least possible perimeter of the triangle?
A) 17 cm
B) 12 cm
C) 14 cm
D) 15 cm

Answer 1

In a triangle, sum of the lengths of any two sides is always greater than the length of the third side. If the sides of a triangle are a, b and c,

a+b>c

Since the side with length 5 is smaller than the side with length 7, let us assume a=5

5+b>c

Let's assume the side with length 7 is the largest side of the triangle. In that case, c=7

Thus, 5+b>7

b>2

Now, let's assume the side with length 7 is NOT the largest side of the triangle. In that case, b=7

Thus, 5+7>c

12>c

c<12

Since, b and c represent the third side of the triangle in the above two cases, the third side lies between 2 and 12

2<thirdside<12
so mim perimeter=5+7+2=14