Question

In triunghiul dreptunghic ABC cu m(A)=90, se dau inaltimea AD=8cm si DB/DC=1/4.Calculati aria si perimetrul ABC rezolvatiiiii

Answer 1

B

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| D

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A___________________C

t.h.=>AD^2=BD•DC

DC=4DB (ip.)

64=4BD^2

BD^2=16 =>BD=4 cm =>DC=16 cm =>BC=20 cm

t.cat.=>AC^2=DC•BC

AC^2=16•20 =>AC=8rad5 cm

AB^2=BD•BC

AB^2=4•20 =>AB=4rad5 cm

P=12rad5+20=4(3rad5+5) cm

A=(8rad5•4rad5)/2=80 cm^2