(C) Let the length of the shortest side be $x \text{ cm}$.The longest side is $2x \text{ cm}$ and the third side is $(x + 2) \text{ cm}$.The perimeter

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(C) Let the length of the shortest side be $x \text{ cm}$.The longest side is $2x \text{ cm}$ and the third side is $(x + 2) \text{ cm}$.The perimeter of the triangle is the sum of all sides: $P = x + 2x + (x + 2) = 4x + 2$.According to the problem, the perimeter is greater than $166 \text{ cm}$:$4x + 2 > 166$Subtract $2$ from both sides:$4x > 164$Divide by $4$:$x > 41$.Since $x$ must be greater than $41$, the minimum integer length of the shortest side is $42 \text{ cm}$.

Class 11 Mathematics Linear Inequalities Word problem of Linear inequalities

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The longest side of a triangle is twice the shortest side and the third side is $2 \text{ cm}$ longer than the shortest side. If the perimeter of the triangle is more than $166 \text{ cm}$, then find the minimum length of the shortest side. (in $\text{ cm}$)

A
$40$
B
$41$
C
$42$
D
$43$

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Word problem of Linear inequalities

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The longest side of a triangle is twice the shortest side and the third side is $2 \text{ cm}$ longer than the shortest side. If the perimeter of the triangle is more than $166 \text{ cm}$, then find the minimum length of the shortest side. (in $\text{ cm}$)

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