Question

5 Dacă ABC si PQR asemenea, AB = 7cm AC=9 cm PR=21cm QR = 36 cm determinati perimetru celor doua triunghiuri (pag 144)​

Answer 1

Răspuns:

Explicație pas cu pas:

Answer 2

Explicație pas cu pas:

ΔABC ~ ΔPQR

$\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AC}{PR} \iff \frac{7}{PQ} = \frac{BC}{36} = \frac{9}{21} = \frac{3}{7}$

$PQ = \frac{7 \cdot 7}{3} = \frac{49}{3} \: cm \\ BC = \frac{36 \cdot 3}{7} = \frac{108}{7} \: cm$

→

$P(\triangle ABC) = AB + AC + BC = 7 + 9 + \frac{108}{7} = \frac{220}{7} \: cm$

$P(\triangle PQR) = PQ + PR + QR = \frac{49}{3} + 21 + 36 = \frac{220}{3}$