a)
ΔADE~ΔACB (U.U)⇒
[tex]\frac{AD}{AC}=\frac{AE}{AB}=\frac{DE}{BC}\\\\ \frac{12}{36}=\frac{AE}{27}=\frac{DE}{48}[/tex]
[tex]AE=\frac{12\cdot 27}{36}= 9\ cm[/tex]
[tex]DE=\frac{48\cdot 12}{36}= 16\ cm[/tex]
[tex]P_{ADE}=AD+DE+AE=12+9+16=37\ cm[/tex]
b)
Daca doua triunghiuri sunt asemenea, atunci raportul ariilor va fi egal cu patratul raportului de asemanare, astfel vom avea:
[tex]\frac{A_{ADE}}{A_{ACB}}=(\frac{AD}{AC})^2\\\\ \frac{A_{ADE}}{A_{ACB}}=(\frac{12}{36})^2=\frac{1}{9}\\\\ A_{ACB}=9A_{ADE}\\\\A_{DECB}= A_{ACB}-A_{ADE} \\\\A_{DECB}=9A_{ADE}-A_{ADE}=8A_{ADE}[/tex]
[tex]A_{ADE}=\frac{1}{8}A_{DECB}[/tex]
[tex]\frac{p}{100}=\frac{1}{8}\\\\ p= 12,5%[/tex]
Un alt exercitiu de geometrie gasesti aici: https://brainly.ro/tema/1799331
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