AB=18 cm
AC=24 cm
BD=12 cm
a)
Aflam BC din Pitagora (suma catetelor la patrat este egala cu ipotenuza la patrat)
BC²=AB²+AC²
BC²=324+576
BC²=900
BC=30 cm
CD=BC-BD
CD=30-12=18 cm
BE²=BD²+DE²
BE²=144+DE²
BE²=AB²+AE²
BE²=324+AE²
144+DE²=324+AE²
DE²=180+AE² (1)
DE²=CE²-CD²
DE²=(AC-AE)²-324
DE²=576-48AE+AE²-324 (2)
Din (1) si (2) ⇒ 576-48AE+AE²-324=180+AE²
252-48AE=180
72=48AE
AE=1,5 cm
EC=24-1,5=22,5 cm
DE²=180+2,25
DE=13,5 cm
[tex]P_{CDE}=13,5+22,5+18=54\ cm[/tex]
b)
Notam DM⊥AC
DM este inaltime in ΔCDE dreptunghic
[tex]DM=\frac{DE\cdot DC}{CE} =\frac{13,5\cdot 18}{22,5} =10,8\ cm[/tex]
SAU
AB║DM
ΔCDM~ΔCBA
[tex]\frac{CD}{CB} =\frac{CM}{CA}=\frac{DM}{AB} \\\\\frac{18}{30}=\frac{CM}{24}=\frac{DM}{18}\\\\ DM=\frac{324}{30} = 10,8\ cm[/tex]
Un alt exercitiu de geometrie gasesti aici: https://brainly.ro/tema/605446
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