1 of 8 0-day streak

Applied similarity and scale

Question 1 of 8

No calculator

A scale relation is used in a triangular garden layout with an inner boundary

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 corresponding angles of triangles \(FGH\) and \(FJK\) are equal

The known corresponding sides are \(FH=13\ \mathrm{cm}\) and \(FK=52\ \mathrm{cm}\)

The target side \(FG\) is \(7\ \mathrm{cm}\). Its corresponding side \(FJ\) is unknown

Calculate \(FJ\) in \(\mathrm{cm}\)