Triangle perimeter

Geometry Level 2

$ABC$ is a (non-degenerate) triangle with integer sides. Given that $AC$ is the longest side and $AC = 48$ , what is the minimum perimeter of $ABC$ ?

Details and assumptions

A degenerate triangle has no area, hence is a straight line.

98 97 96 99

1 solution

Arron Kau Staff
May 13, 2014

By the triangle inequality, we know that $AB + BC > AC = 48$ . Since the lengths are integers, hence $AB + BC \geq 49$ . This can be achieved in a triangle with sides $24 - 25 - 48$ . Hence, the minimum perimeter is $49 + 48 = 97$ .

Triangle perimeter

1 solution

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