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The Longest Side of a Triangle is Three Times the Shortest Side and Third Side is 2 Cm Shorter than the Longest Side If the Perimeter of the Triangles at - Mathematics

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

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Let the shortest side of the triangle be x cm.
Then, the longest side will be 3x and the third side will be 3x − 2. 

\[\therefore \text{ Perimeter of the triangle } \geq 61\]
\[ \Rightarrow x + 3x + 3x - 2 \geq 61\]
\[ \Rightarrow 7x \geq 61 + 2\]
\[ \Rightarrow x \geq 9 (\text{ Dividing throughout by } 7)\]
\[\text{ Hence, the minumum length of the shortest side is 9 cm } .\]

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RD Sharma Class 11 Mathematics Textbook
Chapter 15 Linear Inequations
Exercise 15.4 | Q 9 | Page 24
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