Question:
The longest side of a triangle is twice the shortest side and the third side is 2 cm longer than the shortest side. If the perimeter of the triangle is more than 166 cm then find the minimum length of the shortest side.
Solution:
Let the length of shortest side = ‘x’ cm
According to the question,
The longest side of a triangle is twice the shortest side
⇒ Length of largest side = 2x
Also, the third side is 2 cm longer than the shortest side
⇒ Length of third side = (x + 2) cm
Perimeter of triangle = sum of three sides
= x + 2x + x + 2
= 4x + 2 cm
Now, we know that,
Perimeter is more than 166 cm
⇒ 4x + 2 ≥ 166
⇒ 4x ≥ 164
⇒ x ≥ 41
Hence, minimum length of the shortest side should be = 41 cm.