Question

Fie triunghiul dreptunghic DEF (m(E)=90°), EM⊥DF, M∈DF. Daca DF = 100 cm si $\frac{DM}{MF}= \frac{9}{16}$, calculati lungimea segmentului [EM].

Answer 1

DM + MF = 100 cm
$DM=\frac{9MF}{16}$
$\frac{9MF}{16}+MF=100~cm$
$\frac{25MF}{16}=100~cm$
$25MF=1600~cm$
$MF=64~cm$
$DM=36~cm$
$EM=\sqrt{DM\cdotMF}=\sqrt{36\cdot64}=\sqrt{6^2\cdot8^2}=\sqrt{48^2}=48~cm$