Question

2.Fie Δ dreptunghic ABC cu m(<A)=90 si D proiectia ortogonala a varfului A pe ipotenuza
 b)Daca BD= 5√2cm si AB=10 cm,calculati CD si AC.
c) Daca CD=√15 cm si AC 3√10 cm,calculati BC si AB.
d) Daca AB=24 cm si BC=48 cm,calculati BD si AC.

Answer 1

b) AD=√[10²-(5√2)²] = √(100-50)=5√2
AD²=5√2 × x
50=5√2 × x
x=50/5√2=10/√2=10√2/2=5√2
AC=5√2+5√2=10√2

c) AD=√[(3√10)²-(√15)²] = √(90-15)=√75=5√3
AC²=√15 × BC
90=√15 × BC
BC=90/√15=90√15/15=6√15
AB=√(5√15x6√15)= √450=15√2

d) AC=√48²-24²=√2304-576=√1728=24√3
AB²=48 × BD
576=48 × BD
BD= 576:48=12