Question

Seja AB = 6 cm, AC = 10 cm e BC = 14 cm, e sabendo que o segmento BD tem o triplo da medida do
segmento BM, e que o segmento CF tem o dobro da medida de MC, a soma das medidas de BD e
CF é


(A)
17,5 cm.
hic
(B)
28,75 cm.
(C)
33,25 cm.
(D)
35,5 cm.

Answer 1

$\boxed{\begin{array}{l}\underline{\rm observe~a~figura~que~anexei}\\\sf o~exerc\acute icio~consiste~em~calcular~o~valor~de~3x+2y.\\\sf\dfrac{6}{10}=\dfrac{x}{y}\\\sf \dfrac{x}{6}=\dfrac{y}{10}=k\implies x=6k~~y=10k\\\sf x+y=14\\\sf 6k+10k=14\\\sf 16k=14\\\sf k=\dfrac{14\div2}{16\div2}=\dfrac{7}{8}\end{array}}$

$\large\boxed{\begin{array}{l}\sf x=\diagdown\!\!\!\!6^3\cdot\dfrac{7}{\diagdown\!\!\!\!8_4}=\dfrac{21}{4}\\\\\sf y=\diagdown\!\!\!\!\!\!10^5\cdot\dfrac{7}{\diagdown\!\!\!\!8_4}=\dfrac{35}{4}\\\sf 3x+2y=3\cdot\dfrac{21}{4}+2\cdot\dfrac{35}{4}\\\sf 3x+2y=\dfrac{63}{4}+\dfrac{70}{4}\\\\\sf 3x+2y=\dfrac{133}{4}\\\\\sf 3x+2y=33,25~cm\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~C}}}}\end{array}}$