Question

intr-un triunghi dreptunghic ABC, m(∡A)=90°, AD⊥Bc, D∈(BC) se dau;
a) AB=18 cm si BC=30cm. Calculati BD,CD si AC
b) BD=36cm si AB=60cm. Calculati BC, CD si AC
,

Answer 1

a)
AB=18 cm
BD=30 cm
AC=√(30²-18²)=√(900-324)=√576=24 cm
A=18×24/2=216 cm²
A=30×AD/2    AD=216×2/30=14,4 cm
BD=√(18²-14,4²)=√(324-207,36)=√116,64=10,8 cm
CD=30-10,8=19,2 cm


b)
BD=36 cm
AB=60 cm
AD=√(60²-36²)=√(3600-1296)=√2304=48 cm
AD²=BD×CD
48²=36×CD
CD=2304/36=64 cm
BC=36+64=100 cm
AC=√(48²+64²)=√(2304+4096)=√6400=80 cm