Mathematics

Problem

Two triangles, A and B, each have perimeter

36\,\text{cm}

. Triangle A has sides

14\,\text{cm}

12\,\text{cm}

and

10\,\text{cm}

. Triangle B has sides

16\,\text{cm}

10\,\text{cm}

and

10\,\text{cm}

. (i) Which triangle has its side lengths closer to being equal? (ii) Without carrying out detailed numerical area calculations, explain logically which triangle is expected to enclose the greater area. Give clear reasons based only on the given side lengths.

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