Constructed 77874

Squares are constructed above the overhangs and the transom. Connecting the outer vertices of adjacent squares creates three triangles. Prove that their contents are the same.

Correct answer:

x = 1

Step-by-step explanation:

$$\begin{gathered} a,b,c \\ {c}^2=a^2+b^2 \\ \alpha +\beta =90{}^{\circ } \\ \sin \beta =b:c \\ \sin \alpha =a:c \\ {S}_1=\frac{a\cdot b}{2} \\ {S}_2=\frac{c\cdot b\cdot \sin \alpha }{2} \\ {S}_3=\frac{c\cdot a\cdot \sin \beta }{2} \\ {S}_1=\frac{a\cdot b}{2} \\ {S}_2=\frac{c\cdot b\cdot a/c}{2} \\ {S}_3=\frac{c\cdot a\cdot b/c}{2} \\ {S}_1=\frac{a\cdot b}{2} \\ {S}_2=\frac{a\cdot b}{2} \\ {S}_3=\frac{a\cdot b}{2} \\ {S}_1=S_2 \\ x=1 \end{gathered}$$

Try another example