Sum

The longest side of a triangle is twice the shortest side and the third side is 2cm 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.

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#### Solution

Let the shortest side be x.

Then longest side length = 2x and third side length = x + 2

∴ Perimeter = x + 2x + x + 2

= 4x + 2

Given, perimeter > 166

∴ 4x + 2 > 166

∴ 4x > 166 − 2

∴ 4x > 164

∴ x > 41

The minimum length of the shortest side is 41 cm.

Concept: Linear Inequality

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