$??解：存在??$
$??因?yàn)檎叫蜛BCD的邊長為4\ \mathrm {cm}??$
$??所以AD=CD=4\ \mathrm {cm}，∠ADC= 90°??$
$??因?yàn)镈F⊥DE??$
$??所以∠EDF=90°??$
$??所以∠ADE=∠CDF??$
$??①當(dāng)\frac {AD}{CD}=\frac {DE}{DM}時， △ADE∽△CDM??$
$??因?yàn)锳D=CD=4\ \mathrm {cm}，DE=3\ \mathrm {cm}??$
$??所以\frac {4}{4}=\frac {3}{DM}??$
$??所以DM= 3\ \mathrm {cm}??$
$??②當(dāng)\frac {AD}{DM}=\frac {DE}{CD}時，△ADE∽△CDM??$
$??因?yàn)锳D=CD=4\ \mathrm {cm}，DE= 3\ \mathrm {cm}??$
$??所以\frac {4}{DM}=\frac {3}{4}??$
$??所以DM =\frac {16}{3}\ \mathrm {cm}??$
$??綜上所述，存在點(diǎn)M使得以C、D、M為頂點(diǎn)的三角形與△ADE??$
$??相似，此時DM的長為3\ \mathrm {cm}或\frac {16}{3}\ \mathrm {cm}??.$
