Two polygons are congruent and the perimeter of the first polygon is 39 cm. If the sides of the second polygon are consecutive integers (x, x+1, x+2, x+3, etc.), what value of x makes the polygons into congruent triangles? Use x as the smallest side.

Question

parthkohli · Answer

'Triangle' - this means that there are three sides. If there are 3 sides that are consecutive integers, then the sides would be $x, x+1, x + 2$. We know that the sum of the length of sides is known as the perimeter. We also know that the perimeter of two congruent triangles is the same. So -

$ \color{Black}{\Rightarrow x + (x + 1) + (x + 2) = 39 }$
$ \color{Black}{\Rightarrow 3x  + 3 = 39 }$

Solve for $x$.