Question

In ΔABC ,cu m (A) = 90 ° construim inaltimea AD, D ∈ (BC)
BD=4 cm
CD=16 cm
Aria ΔABC =?
Perimetrul ABC =?

Answer 1

In ΔABC avem:
h = AD, D ∈ BC
BD = 4 cm
CD = 16 cm
=>BC = 4 + 16 = 20 cm

Aplicam teorema catetei pentru a afla catetele:
AB² = BD × BC = 4 × 20 = 80
AB = √80 = 4√5 cm

AC² = CD × BC = 16 × 20 = 320
AC = √320 = 8√5 cm

A = AB × AC / 2 = 4√5 × 8√5 / 2 = 160 / 2 = 80 cm²

P = 20 + 4√5 + 8√5 = 20 + 12√5 cm