Question

The longest side of a triangle is 2 times the shortest side and the third side is 4 cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.

(a) 7

(b) 9

(c) 11

(d) 13

This question was posed to me in an interview for job.

Asked question is from Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation topic in division Linear Inequalities of Mathematics – Class 11

Answer 1

Right choice is (d) 13

The best explanation: Let shortest side be x. Then longest side = 2x.

Third side = 2x-4.

Given, perimeter of triangle is at least 61 cm

=>x+2x+2x-4 ≥ 61 => 5x≥65 = x≥13.

Minimum length of the shortest side is 13 cm.