The longest sides of a triangle is 3 times the shortest side and 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.

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Solution

Let the length of the shortest side be x cm.

Then length of longest side =3x cm

length of third side =(3x-2)cm

Perimeter of triangle =x+3x+3x-2

=(7x-2)cm

Now $7 x - 2 \geq 61 \Rightarrow 7 x \geq 61 + 2$

$\Rightarrow 7 x \geq 63 \Rightarrow x \geq 9$

Thus the minimum length of shortest side =9 cm.

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Q. 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.

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.

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The longest sides of a triangle is 3 times the shortest side and 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.

Let the length of the shortest side be x cm. Then length of longest side =3x cm length of third side =(3x-2)cm Perimeter of triangle =x+3x+3x-2 =(7x-2)cm Now 7x−2≥61⇒7x≥61+2 ⇒7x≥63⇒x≥9 Thus the minimum length of shortest side =9 cm.