AB=20 cm
AC=25 cm
BC=30 cm
AD=10 cm
∡AED=∡ABC
∡A unghi comun ⇒ΔAED~ΔABC
[tex]\frac{AE}{AB}=\frac{AD}{AC}=\frac{ED}{BC}[/tex]
[tex]\frac{AE}{20}=\frac{10}{25}=\frac{ED}{30}[/tex]
AE=8 cm
ED=12 cm
Perimetrul ΔAED=AE+ED+AD=8+12+10=30 cm
[tex]A_{ABC}=\sqrt{p(p-a)(p-b)(p-c)}\\\\ p=\frac{20+25+30}{2} =\frac{75}{2}\\\\ A_{ABC}=\sqrt{\frac{75}{2}\cdot \frac{15}{2}\cdot \frac{25}{2}\cdot \frac{35}{2}}\\\\A_{ABC}=\frac{375\sqrt{7} }{4} \ cm^2[/tex]
[tex]A_{ADE}=\sqrt{15(15-8)(15-12)(15-10)} =\sqrt{15\cdot 7\cdot 3\cdot 5} =15\sqrt{7}\ cm^2[/tex]
[tex]A_{BDEC}=A_{ABC}-A_{ADE}=\frac{315\sqrt{7} }{4}\ cm^2\\\\ \frac{A_{BDEC}}{A_{ABC}} =84\%[/tex]
Un alt exercitiu de geometrie gasesti aici: https://brainly.ro/tema/9959858
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