Question

tie ABCD trapez isoscel, AB || CD . Daca AC perpendicular pe CB, AC=12cm si AB=16 cm,calculati perimetrul si aria trepezului.

Answer 1

AC perpendicular pe CB ⇒ CB²=AB²-AC²=256-144=112 ⇒ CB=AD=√112=4√7 cm.
Ducem CE perpendicular pe AB:
ΔACB asemenea cu ΔCBE(<B comun, <ACB=<CEB=90) ⇒ CE/AC=CB/AB=BE/BC ⇒
CE=AC·CB/AB=12·4√7/16=3√7 cm.
In ΔCBE, BE²=CB²-CE²=112-63=49 ⇒ BE=7 cm ⇒ CD=AB-2BE(trapez isoscel)=2 cm.
P(ABCD)=16+2+2·4√7=18+8√7 cm.
A(ABCD)=(AB+CD)·CE/2=27√7 cm².