Question

Perimetrul paralelogramului ABCD este 54 cm,iar AB=0,8BC. Latura CD are lungimea de:

Repede, va rog ❤️​

Answer 1

Răspuns:

AB=0,8·BC

Perimetrul ABCD=0,8·BC+0,8·BC+BC+BC

Perimetrul ABCD=1,6·BC+2·BC

Perimetrul ABCD=3,6·BC

3,6·BC=54

BC=54:3,6

BC=15 cm

AB=CD=0,8·BC

AB=CD=0,8·15

AB=CD=12 cm

Answer 2

Răspuns: CD=12 cm

Explicație pas cu pas:

$P_{ABCD}=2(L+l)=2(AB+BC)=2(0,8BC+BC)=2\cdot1,8BC=3,6BC\\P_{ABCD}=54 cm\\\\=>3,6BC=54~cm\\\\BC=\frac{54}{3,6}~cm\\\\BC=\frac{540}{36}~cm\\\\BC=15~cm=>AB=0,8\cdot15~cm=\frac{8}{10}\cdot15~cm=\frac{4}{\not{5}}\cdot{\not{15}}~cm=12~cm\\\\CD=AB=12~cm$