Applied similarity and scale
A scale relation is used in a triangular panel plan with a nested panel
Triangle \(FGH\) is inside triangle \(FJK\). Points F, G and J lie in that order on one straight side; F, H and K lie in that order on the other. Side \(FG\) corresponds to side \(FJ\), and side \(FH\) corresponds to side \(FK\)
The sides \(GH\) and \(JK\) are parallel, so the corresponding angles are equal
The known corresponding sides are \(FH=13\ \mathrm{cm}\) and \(FK=52\ \mathrm{cm}\)
The target side \(FG\) is \(14\ \mathrm{cm}\). Its corresponding side \(FJ\) is unknown
Calculate \(FJ\) in \(\mathrm{cm}\)