已知:CD是RT△ABC斜边的高,AB=5,BC=4.求S△ABC:S△ACD:S△BCD

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/29 20:25:28
已知:CD是RT△ABC斜边的高,AB=5,BC=4.求S△ABC:S△ACD:S△BCD
x?N0Ư„ TۑbJ~'.@Q+.#CZ$&PG" à6 Wc=l'z}M>O ^Wr|y?((Yx8wS`juz'kG^~R!rltך 7'Y^HN,fWE@ /'y5=orAQZ(EaʘpA-aDM&ø6=D(M"$ `,XM*68k%f)e{^2Bun_B07P;d7 

已知:CD是RT△ABC斜边的高,AB=5,BC=4.求S△ABC:S△ACD:S△BCD
已知:CD是RT△ABC斜边的高,AB=5,BC=4.求S△ABC:S△ACD:S△BCD

已知:CD是RT△ABC斜边的高,AB=5,BC=4.求S△ABC:S△ACD:S△BCD
角ACB为直角.
AC²+BC²=AB²得:
AB=3
△ABC与△ACD相识得:
CD:BC=AD:AC=AC:AB=4:5
得:CD=(4/5)*3=12/5
AD=(4/5)*4=16/5
S△ACD=CD*AD/2=96/25
△ABC与△BCD相识得:
CD:AC=BD:BC=BC:AB=3:5
得:CD=(3/5)*4=12/5
BD=(3/5)*3=9/5
S△BCD=CD*AD/2=54/25
S△ABC=AC*BC/2=6
S△ABC:S△ACD:S△BCD
=6:96/25:54/25
=1:16/25:9/25
=25:16:9
=5²:4²:3²