Question

intr-un triunghi,ABC,AB=26,BC= 28 AC = 30 BDPERPENDICULAR PE AC, BD=?

Answer 1

 

$\displaystyle\\\text{Calculam aria triunghiului cu formula lui Heron.}\\\\P=AB+BC+AC =26+28+30=84~\text{cm}\\\\p= \frac{P}{2}=\frac{84}{2}=42~\text{cm}\\\\A=\sqrt{p(p-AB)(p-AC)(p-BC)}=\\\\=\sqrt{42(42-26)(42-30)(42-28)}=\\\\=\sqrt{42\times16\times 12\times14}=\\\\=\sqrt{7\cdot6\times4\cdot4\times 2\cdot6\times2\cdot7}=\\\\=\sqrt{7^2\times6^2\times4^2\times 2^2}=7\times6\times4\times 2=336\text{ cm}^2$

$\displaystyle\\\\\text{Scriem formula de calcul a ariei folosind baza si inaltimea in care }\\\text{baza si aria sunt cunoscute si inaltimea BD este necunoscuta.}\\\\A=\frac{Baza \times Inaltimea}{2}\\\\A=frac{AC \times BD}{2}\\\\336=\frac{30 \times BD}{2}\\\\BD=\frac{2\times336}{30}=\frac{672}{30}=\frac{224}{10}=\boxed{\bf22,\!4\text{ cm}}$