Question

Va rog multt !
Raportul catetelor unui triunghi dreptunghic este 8/15 si perimetrul triunghiului are 160 cm . Calculati :
A)lungimea catetelor
B) lungimea ipotenuzei
C) lungimea inaltimii corespunzatoare ipotenuzei .

Answer 1

c1/c2=8/15=>15c1=8c2=k=>c1=k/15;c2=k/8;i=sqrt(k^2/225+k^2/64); P=i+c1+c2=k/15+k/8+sqrt(k^2/225+k^2/64)=160cm.; 23k/120+sqrt(289k^2/14400)=160; 23k/120+17k/120=160; 40k/120=160; k=160•120/40=480; c1=32cm; c2=60cm; i=68cm; Notam AD inaltime,BC -ipotenuza ;AB =c1;AC=c2.Scriem teorema catetei:AB^2=BC•BD=>BD=AB^2/BC;AC^2=BC•DC=>DC=AC^2/BC;Scriem teorema inaltimii:AD^2=BD•DC=AB^2/BC•AC^2/BC=(AB^2•AC^2)/BC^2=>AD=(AB•AC)/BC=28,23cm