Explanation:
We are given the diagram of a triangle, so we know:
[tex]h=40 \\ \\ s_{1}=20[/tex]
From the diagram:
[tex]s_{1}+s_{2}=h \\ \\ Isolating \ s_{2}: \\ \\ s_{2}=h-s_{1} \\ \\ s_{2}=40-20 \\ \\ s_{2}=20[/tex]
By Pythagorean Theorem:
[tex]s_{1}^2+a^2=u_{1}^2 \rightarrow 20^2+a^2=u_{1}^2 \\ \\ s_{2}^2+a^2=u_{1}^2 \rightarrow 20^2+a^2=u_{2}^2 \\ \\ \\ From \ here: \\ \\u_{1}=u_{2}[/tex]
So this is a 45-45-90 triangle. Thus:
[tex]If \ u_{1}=u_{2}=x \ then: \\ \\ \\ h=x\sqrt{2} \therefore 40=x\sqrt{2} \therefore x=20\sqrt{2}[/tex]
So:
[tex]u_{1}=u_{2}=20\sqrt{2}[/tex]
Also, by Pythagorean Theorem:
[tex]a=\sqrt{u_{1}^2-s_{1}^2} \\ \\ a=\sqrt{(20\sqrt{2})^2-20^2}=20[/tex]
Finally:
[tex]\boxed{s_{2}=20} \ \ \ \boxed{a=20} \ \ \ \boxed{u_{1}=20\sqrt{2}} \ \ \ \boxed{u_{2}=20\sqrt{2}}[/tex]
