Question

In figura alaturata HG||EF. Calculati perimetrul triunghiului DHG. Va rog repede!

Answer 1

Triunghiurile DHG si DEF sunt asemenea
$\frac{DH}{DE}=\frac{DG}{DF}=\frac{HG}{EF} \\ \\ \frac{DH}{DH+9}=\frac{DG}{DG+6}=\frac{4}{10}$
$10\cdot DH=4(DH+9) \\ \\ 10\cdot DH=4\cdot DH+36 \\ \\ 6\cdot DH=36 \\ \\ DH=6$
$10\cdot DG=4(DG+6) \\ \\ 10\cdot DG=4\cdot DG+24 \\ \\ 6\cdot DG=24 \\ \\ DG=4$
$P_{\triangle DHG}=DH+DG+HG=6+4+4=14$