The perimeter of a triangle is 126 inches. The longest side is 7 inches longer than the shortest side. The shortest side is 2 inches less than remaining side. Find the length of the shortest side.

Answer 1

The shortest side is 39 inches.

Let the 3 sides be a, b, and c where a is the longest and c the shortest.

By the question,

c+7 = a
c+2 = b

From the above information, we can calculate that,

a-5=b
a=5+b ----- equation (i)

Similarly,

a+b+c=126
c=126-a-b
a-7=126-a-b [since c+7=a, by the question so c=a-7.]
a+a=126+7-b
2a=133-b
2(5+b)=133-b
10+2b=133-b
2b+b=133-10
3b=123
b=123/3
b=41

Applying the value of b=41 in c+2=b, as it is given in the question.

c=b-2
c=41-2
c=39.

So the length of the shortest side is 39 inches.