Question

1.In triunghiul ABC cu m(a)=90 grade ,construim inaltimea AD, D e(BC) stiind ca :
a) CD=6 cm,BC=24 cm calculati AC
b)BD=3 cm,BC=15 cm calculati AB

2.In triunghiul ABC m(a)=90 grade construim inaltimea AD, D e (BC) stiind ca AC=12 cm si CD=16 cm calculati BD

3.In triunghiul ABC cu m(a)=90 grade construim inaltimea AD, D e (BC) stiind ca AC=18 cm,BC=36 cm,calculati BD

VA ROOOG!!!
DAU COROANE​

Answer 1

Răspuns:

1.

a) AC= 12 cm

b)

$AB= \: 3 \sqrt{5}$

2. DB= 7 cm

3.

$AB =\:18 \sqrt{3} cm$

Explicație:

1.

a)

${AC}^{2} = CD \times CB$

${AC}^{2} = 6 \times 24 \\ {AC}^{2} = 144 \\ AC = \sqrt{144} = 12 \: cm$

b)

${AB}^{2} = BD \times BC \\ {AB}^{2} = 3 \times 15 \\ AB = \sqrt{45} = 3 \sqrt{5} cm$

2.

CB = CD + DB

${AC}^{2} = DC \: \times BC \\ {AC}^{2} = DC \: \times (DC +BD) \\ {12}^{2} = 16 \times (16 +BD) \\ 144 = 256 + 16BD \\ 256 - 144 = 16BD \\ 112 = 16BD \\ BD = 112 \div 16 = 7cm$

3.

ABC: m(A)=90° =>

${AB}^{2} = {BC}^{2} - {AC}^{2} \\ {AB}^{2} = {36}^{2} - {18}^{2} \\ {AB}^{2} = 1296 - 324 \\ AB = \sqrt{972} = 18 \sqrt{3} cm$