[tex]h^{2} +6^{2} =7^{2} \\h^{2} =7^{2}- 6^{2} \\h^{2}=49-36\\ h^{2} =13\\h=\sqrt{13} \\(\sqrt{13} )^{2} +5^{2} =x^{2} \\13+25=x^{2} \\38=x^{2} \\x=\sqrt{38}\\\\[/tex]
[tex]4^{2} +h^{2} =8^{2} \\h^{2} =8^{2}-4^{2} \\h^{2} =64-16\\h^{2} =48\\h=\sqrt{48} =4\sqrt{3} \\(4+y)^{2} +(4\sqrt{3} )^{2} =13^{2} \\16+8y+y^{2} +48=169\\y^{2} +8y-105=0\\[/tex]
Δ[tex]=b^{2} -4ac=8^{2} -4*1*(-105)=64+420=484\\[/tex]
√Δ[tex]=22[/tex]
[tex]y_{1} =\frac{-8-22}{2*1} =\frac{-30}{2} =-15[/tex] - nie możliwe aby bok miał wartość -15
[tex]y_{2} =\frac{-8+22}{2*1} =\frac{14}{2} =7[/tex]
y = 7
