# 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 - Mathematics

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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.

#### Solution

Let the length of shortest side = ‘x’ cm

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.

Concept: Inequalities - Introduction
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#### APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 6 Linear Inequalities
Exercise | Q 11 | Page 107
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