The longest side of a triangle is three times the shortest side and the third side is $2$ cm 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

The correct option is A $9$ cm
Let the shortest side $= s$
Longest side $= 3 s$
Third side $= 3 s - 2$
Now perimeter $= s + 3 s + 3 s - 2 = 7 s - 2 \geq 61$
$∴ 7 s \geq 63$
$∴ s \geq 9$
Thus minimum length of the shortest side $= 9$ cm

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The longest side of a triangle is three times the shortest side and the third side is 2 cm 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 cmLet the shortest side =sLongest side =3sThird side =3s−2Now perimeter =s+3s+3s−2=7s−2≥61∴7s≥63∴s≥9Thus minimum length of the shortest side=9 cm

The longest side of a triangle is three times the shortest side and the third side is $2$ cm 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 shortest side $= s$
Longest side $= 3 s$
Third side $= 3 s - 2$
Now perimeter $= s + 3 s + 3 s - 2 = 7 s - 2 \geq 61$
$∴ 7 s \geq 63$
$∴ s \geq 9$
Thus minimum length of the shortest side $= 9$ cm