Q11 of 32 Page 107

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.

Let the length of shortest side be ‘x’ cm


Given, 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, perimeter is more than 166 cm


⇒ 4x + 2 ≥ 166


⇒ 4x ≥ 164


⇒ x ≥ 41


Hence, minimum length of the shortest side should be 41 cm.


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