Question

va rog ajutor la ex 5​

Answer 1

a)

MR = MN-RN = 14 - 10 = 4 cm

$\dfrac{MR}{MN} = \dfrac{MT}{MP} \iff \dfrac{MR + MN}{MN} = \dfrac{MT + MP}{MP}$

$\dfrac{4 + 14}{14} = \dfrac{24}{MP} \iff \dfrac{18}{14} = \dfrac{24}{MP}$

$MP = \dfrac{14 \cdot 24}{18} \implies MP = \dfrac{56}{3} \ cm$

b)

$\dfrac{MN}{MR} = \dfrac{MP}{MT} \iff \dfrac{13}{8} = \dfrac{MP}{MT}$

$\dfrac{13 - 8}{8} = \dfrac{MP - MT}{MT} \iff \dfrac{5}{8} = \dfrac{TP}{MT}$

$\dfrac{5}{8} = \dfrac{15}{MT} \iff MT = \dfrac{8 \cdot 15}{5}$

$\implies MT = 24 \ cm$