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(A) Let the shortest side of the triangle be $x 	ext{ cm}$.According to the problem, the longest side is $2x 	ext{ cm}$ and the third side is $(x +

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(A) Let the shortest side of the triangle be $x 	ext{ cm}$.According to the problem, the longest side is $2x 	ext{ cm}$ and the third side is $(x + 3) 	ext{ cm}$.The perimeter of the triangle is the sum of its three sides:$P = x + 2x + (x + 3) = 4x + 3$.Given that the perimeter is at least $51 	ext{ cm}$, we have the inequality:$4x + 3 \geq 51$.Subtracting $3$ from both sides:$4x \geq 48$.Dividing by $4$:$x \geq 12$.Thus, the minimum length of the shortest side is $12 	ext{ cm}$.

The longest side of a triangle is twice the shortest side and the third side is $3 \text{ cm}$ more than the shortest side. If the perimeter of the triangle is at least $51 \text{ cm}$, find the minimum length of the shortest side. (in $\text{ cm}$)

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