Question

In triunghiul dreptunghic ABC , m( A)=90° , AD perpendicular pe BC , D∈(BC), se cunosc lungimile a doua segmente : AD=7 cm si BC = 50 cm. Calculati:AB,AC,BD

Answer 1

notam DC=x
BD=50-x
AD²=BD×DC
7²=x(50-x)
49=50x-x²
x²-50x+49=0
x²-x-49x+49=0
x(x-1)-49(x-1)=0
(x-1)(x-49)=0
DC=x=1  ⇒  BD=50-1=49 cm
AB=√(49²+7²)=√2450=35√2 cm
AC=√(7²+1²)=5√2 cm