The perimeter of a given triangle, whose sides are in the ratio of \(3 : 4 : 5\), is greater by \(\quantity{4}{ft.}\) than that of a given square. The area of the square is greater by \(\quantity{25}{sq.ft.}\) than that of the triangle. Find the lengths of the sides of the square and of the triangle.

What do we know about a triangle with side lengths 3, 4 and 5?

Can we use the information in the question to form a pair of simultaneous equations?

In this applet, the perimeters differ by \(4\) and the sides of the triangle are \(3a\), \(4a\) and \(5a\).