Question

ajutați-mă ex 14.........​

Answer 1

Răspuns:

a) BC=250cm; BD=230,4cm; AD=67,2cm; AB=240cm

b)BC=100 cm; $AB=20\sqrt{5} cm$; $AC=40\sqrt{5} cm$; AD=40cm

Explicație pas cu pas:

-------------------------------------rezolvare a)----------------------------------------------

TEOREMA CATETEI:

AC²=DC*BC

4900=19,6*BC

BC=250

BC=BD+DC

BD=250-19,6=230,4

Teorema inaltimii:

AD²=BD*CD

AD=$\sqrt{BD*CD}=\sqrt{19,6*230,4} =67,2 cm$

TEOREMA CATETEI:

AB²=BD*BC

$AB=\sqrt{BD*BC}=\sqrt{250*230,4} =240 cm$

----------------------------------------rezolvare b)----------------------------------------

BC=BD+CD=20+80=100cm

TEOREMA CATETEI:

AB²=BD*BC

$AB=\sqrt{BD*BC}=\sqrt{100*20} =20\sqrt{5} cm$

TEOREMA CATETEI:

AC²=DC*BC

$AC=\sqrt{CD*BC}=\sqrt{100*80} =40\sqrt{5} cm$

Teorema inaltimii:

AD²=BD*CD

AD=$\sqrt{BD*CD}=\sqrt{20*80} =40 cm$