Question

in trapezul dreptunghic abcd  cu m(A)=m(D)=90 de grade ab = ad= radical din 3si m(C)=60 de grade.calculati  perimetrul si lungimile diagonalelor trapezului

Answer 1

construiesti inaltimea trapezului: BM
in ΔBMC, mM=90, mC=60⇒mB=30⇒th 30-60-90 MC=BC/2
notezi BC=x⇒MC=x/2
aplici th Pitagora x²=√3²+x²/4
x²-x²/4=3
3x²/4=3
x²=4
x=2=BC
MC=2/2=1
DC=DM+MC
DC=√3+1
P=√3+√3+1+2+√3=3√3+3=3(√3+1)
Afli diagonala BD din tr drept DAB, mA=90, AD=AB=√3⇒DB=√3*√2=√6
Afli diagonala AC din ΔADC, mD=90, AD=√3, DC=√3+1
AC²=√3²+(√3+1)²=3+3+2√3+1=7+2√3
AC=√7+√12