Question

In triunghiul ABC cu AB = 25 cm, AC = 25 cm, in punctul D e [ AB ] astfel incat AD supra BD = 2 supra 3 seduce DE || BC, E e [ AC ] Calculati lungimile lui: AE si EC ; AD si BD

Answer 1

Răspuns:

Explicație pas cu pas:

AB = 25 cm

AC = 25 cm

DE ║ BC

AE = ? EC = ? AD = ? BD ?        

$\large\bf \dfrac{AD}{BD} =\dfrac{2}{3} \implies \dfrac{AD}{AB-AD} =\dfrac{2}{3} \implies 3AD = 2AB-2AD$

$\large\bf 3AD +2AD= 2AB\implies 5AD = 2AB\implies \boxed{\bf \dfrac{AD}{AB} =\dfrac{2}{5}}$

$\large\bf \Delta ADE \sim \Delta ABC\implies \boxed{\bf \dfrac{AD}{AB} =\dfrac{AE}{AC} =\dfrac{DE}{BC}}$

$\large\bf \dfrac{AD}{AB} =\dfrac{AE}{AC}=\dfrac{2}{5} \implies AE = \dfrac{AC \cdot 2}{5} \implies\boxed{\bf AE = 10~cm}$

$\large\bf EC = AC-AE \implies EC = 25-10 \implies \boxed{\bf EC =15~cm}$

$\large\bf \dfrac{AD}{AB} =\dfrac{2}{5} \implies \dfrac{AD}{25} =\dfrac{2}{5} \implies AD = \dfrac{2\cdot 25}{5}\implies \boxed{\bf AD = 10~cm}$

$\large\bf BD = AB-AD \implies BD = 25-10 \implies \boxed{\bf BD =15~cm}$

P.S.: Te rog sa glisezi spre stânga pentru a vedea toata rezolvarea daca esti pe telefon

==pav38==

Answer 2

$\it Vom\ nota\ AD=2k,\ BD=3k,\ unde\ k\in\mathbb{R_+^*} \\ \\ AD+DB=AB \Rightarrow 2k+3k=25 \Rightarrow 5k=25 \Rightarrow k=5$

$\it AD=2k=2\cdot5=10\ cm\\ \\ BD=3k=3\cdot5=15\ cm$