Question

Three squares are placed next to each other as shown. The vertices A, B, and C are collinear. Find the dimension n. Replace the lengths 4 and 7 by m and k, respectively. Express k in terms of m and n.

Answer 1

$\frac{k-m}{m} = \frac{n-k}{k} \\ \\k^2-mk=mn-mk \\k^2=mn \\k= \sqrt{mn}$

$7^2=4n \\ \\n= \frac{49}{4}$