Question

Raportul catetelor unui triunghi dreptunghic este 0,75 iar media are latura la Ipotenuza are lungimea de 10 cm. Calculați perimetrul triunghiului

Answer 1

Presupunem ca triunghiul este dreptunghic in A.
$\frac{AB}{AC} = \frac{75}{100} =\ \textgreater \ \frac{AB}{AC} = \frac{3}{4} =\ \textgreater \ AB= \frac{3AC}{4}$
Mediana (AD) este egala cu jumatate din ipotenuza => $AD= \frac{BC}{2} =\ \textgreater \ BC=2AD=20cm$
Teorema lui Pitagora : $AB^{2} + AC^{2} = BC^{2}$
$(\frac{3AC}{4}) ^{2} + AC^{2} = 400$
$\frac{ 9AC^{2} }{16} + AC^{2} =400$
$\frac{ 25AC^{2} }{16} = 400$
$AC^{2} =400* \frac{16}{25} =\ \textgreater \ AC= \sqrt{400* \frac{16}{25}$
$AC=20* \frac{4}{5} =\ \textgreater \ AC=16$
AB=$\frac{3*16}{4} =12cm$
P=AB+AC+BC=(12+16+20)cm=48cm

Answer 2

AB/AC75/100=3/4
AB/3=AC/4=k
AB=3k
AC=4k
AM-mediana
AM=10cm conf th medianei
BC=20cm
conf th Pitagora in ∆ABC
AB^2+AC^2=BC^2
9k^2+16k^2=400
25k^2=400
k^2=400:25
k^2=16
pt k=4
AB=12cm
AC=16cm
P∆ABC=AB+AC+BC
P∆ABC=12cm+16cm+20cm
P∆ABC=48cm