Question

ajutati maaa ex 8 ..​

Answer 1

Răspuns:

9 cm

Explicație pas cu pas:

T.P.: AB²= BC²-AC² = 20²-16² = 400-256 = 144 = 12² => AB = 12 cm

$\dfrac{AM}{MC} = \dfrac{1}{3} \iff \dfrac{AM + MC}{MC} = \dfrac{1 + 3}{3} \\ \dfrac{AC}{MC} = \dfrac{4}{3} \iff \dfrac{16}{MC} = \dfrac{4}{3} \\ \implies MC = 12 \: cm$

MP || AB => ΔMPC ~ ΔABC

$\dfrac{MP}{AB} = \dfrac{MC}{AC} \iff \dfrac{MP}{12} = \dfrac{12}{16} \\ \implies MP = 9 \ cm$

MP || AB => MP || α

MQ || PS, Q ∈ α, S ∈ α

=> MP || QS => MPSQ este paralelogram

=> MP ≡ QS

=> QS = 9 cm