Question

In trapezul dreptunghic ABCD , Ad||bc ,masura unghiului a si b =90 de grade . Ac perpendicular pe CD ,CD=80 cm , BC =36 cm .
Calculati :
a) perimetrul trapezului abcd .b) lungimea diagonalei ac
Va rog am nevoie urgent

Answer 1

Fie CE⊥AD, CE-intaltime in ΔACD dreptunghic
AECB - dreptunghi⇒ AE= BC=36
Teorema Catetei CD²  = ED * AD⇒ 6400 = ED * (ED+AE)
6400  = ED² + ED*36
ED² + 36ED - 6400=0
ED² +100ED - 64ED-6400=0
ED(ED+100) - 64 ( ED+100)=0
(ED+100)(ED-64)=0⇒ ED-64=0⇒ ED=64 cm
AD=AE+ED=36+64=100 cm
CE² = AE*ED= 36*64⇒ CE=√36*√64= 6*8=48cm = AD
P ABCD = AB+BC+CD+AD= 48+36+80+100 = 264 cm

b) in ΔADC dreptunghic⇒ TP⇒ AC² =AD²-CD² = 10000-6400=3600
AC=60 cm