The longest side of a triangle is 3 times the shorter side and then the third side is 2cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.

9 cm

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6 cm

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8 cm

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None of these

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Solution

The correct option is A
9 cm

Let the length of the shortest side of the triangle be x cm.

Then length of longest side be 3x

Length of the third side = (3x -2) cm

Since the perimeter of the triangle is at least 61 cm.

x cm + 3x cm + (3x -2) cm $\geq$ 61 cm

7x – 2 $\geq$ 61

7x $\geq$ 63

x $\geq$ 9 cm

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The longest side of a triangle is 3 times the shorter side and then the third side is 2cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm, find the minimum length of the shortest side.

The correct option is A 9 cm Let the length of the shortest side of the triangle be x cm. Then length of longest side be 3x Length of the third side = (3x -2) cm Since the perimeter of the triangle is at least 61 cm. x cm + 3x cm + (3x -2) cm ≥ 61 cm 7x – 2 ≥ 61 7x ≥ 63 x ≥ 9 cm