a) Ta có:
\(h^2=b'.c'=36.64=2304\Rightarrow h=48\left(cm\right)\) (định lí 2)
\(b^2=a.b'=\left(b'+c'\right).b'=\left(36+64\right).3600\Rightarrow b=60\left(cm\right)\)(định lí 1)
\(c^2=a.c'=\left(b'+c'\right).c'=\left(36+64\right).64=6400\Rightarrow c=80\left(cm\right)\)
(định lí 1)
Vậy b = 60cm; c = 80cm; h=48
b) Ta có: \(c^2=a.c'\Leftrightarrow6^2=9.c'\Leftrightarrow c'=\dfrac{36}{9}=4\left(cm\right)\)
mà c' + b' = a \(\Rightarrow b'=a-c'=9-4=5\left(cm\right)\)
\(h^2=b'.c'=5.4=20\Rightarrow h=2\sqrt{5}\left(cm\right)\)
Áp dụng định lí Py-ta-go vào tam giác vuông ABC, ta có: \(b^2=a^2-c^2=9^2-6^2=45\Rightarrow b=3\sqrt{5}\left(cm\right)\)
Vậy h = \(2\sqrt{5}cm;b=3\sqrt{5}cm;\) c' = 4cm; b' = 5cm