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第37頁(yè)

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$解：∵?△ABC∽△A'B'C'?$

$∴?\frac {AB}{A'B'}=\frac {AC}{A'C'}=\frac {BC}{B'C'}=\frac {AB+BC+AC}{A'C'+B'C'+A'C'}=\frac {60}{72}?$

$又∵?AB=15\ \mathrm {cm}，??B'C'=24\ \mathrm {cm}?$

$∴?A'B'=18\ \mathrm {cm}，??BC=20\ \mathrm {cm}?$

$解：∵?DE//BC?$

$∴?∠DEB=∠EBC，??∠EDC=∠DCB?$

$∴?△DOE∽△COB?$

$由?△DOE?與?△COB?的面積比為?4：??9?$

$可得?△DOE?與?△COB?的相似比為?2：??3?$

$∴?\frac {DE}{BC}=\frac 23?$

$∵?DE//BC?$

$∴?\frac {AE}{AC}=\frac {DE}{BC}=\frac 23?$

$解：?(1)△ABC?的周長(zhǎng)?=20×\frac 3{3+2}=12(\mathrm {cm})?$

$?△A'B'C'?的周長(zhǎng)?=20×\frac 2{3+2}=8(\mathrm {cm})?$

$?(2)?∵?△ABC?與?△A'B'C'?的相似比為?\frac 32?$

$∴面積比為?\frac 94?$

$∴?S_{△ABC}=5÷\frac {9-4}9=9(\mathrm {cm^2})，??S_{△A'B'C'}=5÷\frac {9-4}4=4(\mathrm {cm^2})?$

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