Question

Triunghiul ABC este dreptunghic in A.
Inaltimea AD are 12cm,iar ipotenuza BC are 25cm. Sa se afle lungimra catetelor

Answer 1

In ▲ABC, m(ADB)=90° si m(BAC)=90°=>(conform teoremei inaltimii) AD=(AB•AC)/BC=> AB•AC=12•25
Notam BD=x=>DC=25-x
(BC=BD+DC)
In ▲ABC, m(A)=90°=>(conform teoremei catetei) AB²=BC•BD=25x
AC²=BC•DC=25(25-x)=625-25x
AB•AC=12•25=>AB²•AC²=12²•25²=>(625-25x)•25x=144• 625=> 25³x-25²x²=25²•144/(÷25²)=>25x-x²=144=> -x²+25x-144=0=> x²-25x+144=0
delta=25²-4•144=>delta=49=7²
x1=(25-7)/2=9
x2=(25+7)/2=16
AB²=9•25=>AB=15 cm
AC²=16•25=>AC=20 cm
AB=15 cm si AC=20 cm SAU AB=20cm si AC=15 cm.
Sper ca te-am ajutat!