Ta đặt : \(AB=20a\) ; \(AC=21a\)
Áp dụng ĐL 4 trong hệ thức lượng giác ta có :
\(\dfrac{1}{AH^2}=\dfrac{1}{AB^2}+\dfrac{1}{AC^2}< =>\dfrac{1}{420^2}=\dfrac{1}{2o^2a^2}+\dfrac{1}{21^2a^2}< =>\dfrac{1}{420^2}=\dfrac{29^2}{420^2a^2}< =>\) \(420^2a^2=29^2420^2< =>420a=29.420< =>420a=12180=>a=29\)
=> \(AB=20.29=580\left(\text{đ}v\text{dd}\right)\)
\(=>AC=21.29=609\left(\text{đ}v\text{dd}\right)\)
Áp dụng Đ lí py - ta - go ta có :
\(BC^2=AB^2+AC^2=>BC=\) \(\sqrt{\left(AB^2+AC^2\right)}=\sqrt{\left(580^2+609^2\right)}=841\left(\text{đ}v\text{dd}\right)\)
=> \(Chu-vi-\Delta ABC-l\text{à}:\)
\(C_{\Delta ABC}=AB+AC+BC=580+609+841=2030\left(\text{đ}v\text{dd}\right)\)
