The lengths of the sides of a triangle are in the ratio 5: 6: 7. describe the length of the longest side if the perimeter is less than 54cm

Adding the parts in the ratio gives 18 so there are two triangles possible with perimeters less than 54cm where the side lengths are all integers: a 5, 6, 7 triangle or a 10, 12, 14 triangle.

Therefore the length of the longest side must be either 7cm or 14cm (unless you want to include non-integer side lengths, then it could also be 3.5cm, 1.75cm etc)

What are the following algebraic equations. you need to post those if you want the answer

Aline graph should be used