Question

Intr-un triunghi dreptunghic ABC, m(≤A)=90, AD perpendicular BC, D apartine BC, se dau: AB=16, BC=20. Se cer BD, DC, AD, AC si Aria tr ABC. Va rog nu stiu acest subpunct

Answer 1

Incepem cu aria

folosind teorema lui pitagora in trg. ABC,<A=90 grade => (din teorema lui pitagora) 400=AC la puterea a 2 a + 256

AC=$\sqrt{144}$

Ac=12 cm

Aria=(Cateta 1 * cateta 2):2=96 cm patrati

Folosind teorema catetei

$AC^{2}$=CD*CB

144=CD*20

CD=$\frac{144}{20}$ (simplificam prin 2)=$\frac{72}{10}$(simplificam iar prin 2)$\frac{36}{5}$=7,2 sau lasam fractie

$AB^{2}$=BD*CB

256=BD*20

BD=256:20=12,8 sau $\frac{64}{5}$

Folosind teorema inaltimii

$AD^{2}$=CD*DB

AD=$\sqrt{92,16}$=9,6sau sub forma de fractie $\frac{96}{10}$