和勾股定理有关的数学题（初二的）！ 初二数学勾股定理难一点的应用题，要有答案。谢谢。
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AC===4\uff08m\uff09\uff0c
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已知，ABCD为正方形，则可以知道DC=CB。而CF=4分之一CD。EB=二分之一BC=CE。而正方形的每个内角为90°，则CFE为直角三角形，利用勾股定理。则CF的平方+CE的平方=EF的平方。换算后就等于4分之一X的平方+2分之一X的平方=EF的平方，就等于16分之一X+4分之一X的平方=16分之五X，则EF的平方就等于16分之五。
同理就出AF的平方，DF=DC-FC=四分之三X。AD=X，则DF的平方+AD的平方=16分之25X=AF的平方。
EB为2分之一X，AB为X。AE的平方=X的平方+二分之一X的平方=4分之五X。
那EF的平方为16分之5。AF的平方为16分之25,，AE的平方为4分之五X就等于16分之20X，EF的平方+AE的平方=AF的平方，满足勾股定理，则AEF为直角三角形
这道题难度其实不大，你可以设正方形边长为X。则CE为X/2，CF为X/4，利用勾股定理可算EF。同理用勾股定理算出AF,AE。看AE,AF,EF是否满足勾股定理即可。若满足，则是直角三角形
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绛旓細1 a^2-10a+25+b^2-24b+144+c^2-26c+169=0 (a-5)^2+(b-12)^2+(c-13)^2=0 鍥犱负骞虫柟涓洪潪璐熸暟 鎵浠 a-5=0 b-12=0 c-13=0 a=5 b=12 c=13 鎵浠 鈻矨BC涓虹洿瑙掍笁瑙掑舰 2 RT鈻矨CD 涓 CD^2+AD^2=AC^2 RT鈻矯BD 涓 CD^2+BD^2=CB^2 RT鈻矨BC 涓 AC^2+BC^2=AB^2...
绛旓細1銆(BC*AC)/2=S鈻矨BC 鎵浠C=(2*30)/12=5cm 鍕捐偂瀹氱悊寰楋細AB=13cm 2銆佸嬀鑲″畾鐞嗗氨涓嶈浜嗗惂 涓変釜杩炵画鍋舵暟鐨勮瘽锛岄偅涔堥兘闄2浠ュ悗蹇呭畾杩樻槸鐩磋涓夎褰紝骞朵笖鏄繛缁嚜鐒舵暟 涔熷氨鏄3锛4锛5 绛旀鏄6锛8锛10
绛旓細璁炬棗鏉嗕负X绫筹紝濡傚浘鎵绀猴紝AC鏄怀瀛愮殑闀垮害锛屽嵆AB+BD=锛圶+3锛夌背锛汢C=9绫 鏍规嵁鍕捐偂瀹氱悊锛屼笁瑙掑舰ABC锛孉B^2+BC^2=AC^2 X^2+9^2=(X+3)^2 X^2+81=X^2+6X+9 X=12
绛旓細AC鐨勪簩娆℃柟+CD鐨勪簩娆℃柟=AD鐨勪簩娆℃柟=25... ...鈶 AC鐨勪簩娆℃柟+CB鐨勪簩娆℃柟=AB鐨勪簩娆℃柟=64... ...鈶 鈶★細AC鐨勪簩娆℃柟+锛圕D+DB锛夌殑浜屾鏂=AB鐨勪簩娆℃柟=64 AC鐨勪簩娆℃柟+CD鐨勪簩娆℃柟+2CD脳DB+DB鐨勪簩娆℃柟=AB鐨勪簩娆℃柟=64 AC鐨勪簩娆℃柟+CD鐨勪簩娆℃柟+10CD+25=64... ...鈶 鈶-鈶...
绛旓細瑙ｏ細璁続D=x锛屽垯CD=12-x FC²=DF²+CD²=16+(12-x)²BC²=36 濡傛灉FC涓烘枩杈癸紝鏈夛細16+(12-x)²=36+x²x=124/24=31/6 濡傛灉浠D涓烘枩杈癸紝鏈夛細x²=16+(12-x)²+36 x=49/6 濡傛灉浠C涓烘枩杈癸紝鏈夛細36=16+(12-x)²+x²...
绛旓細(1)鎶樼棔DE鍦ˋB鐨勫瀭鐩村钩鍒嗙嚎涓婏紝锛屽埄鐢ㄧ浉浼间笁瑙掑舰鍘熺悊鍙緱EF=10/3 (2)鍥犱负BD涓衡垹ABC鐨勫钩鍒嗙嚎銆丏E鈯C銆丆A鈯B , 鎵浠E=DA锛屾墍浠モ柍BAD鍏ㄧ瓑浜庘柍BED.BE=AB=12 鍥犱负鈻矨BC涓虹瓑鑵扮洿瑙掍笁瑙掑舰锛屾墍浠ユ湁AB=AC=12銆丅C=12鍊嶆牴鍙2 鈻矰EC涓虹洿瑙掍笁瑙掑舰锛屾湁 DC^2=DE^2+EC^2鍗筹細锛12-DE)^2=DE^2...
绛旓細浣淎C鍨傜洿浜嶱N锛屼氦鐐笴锛岀洿瑙掍笁瑙掑舰涓紝涓夊崄搴﹁鎵瀵圭殑鐩磋杈圭瓑浜庢枩杈圭殑涓鍗婏紝PA=160锛屾墍浠C=80<100锛屾墍浠ヤ細鏀跺埌褰卞搷銆傚湪PN涓婂彇B銆丏涓ょ偣锛屼娇AB=AD=100锛岀敱鍕捐偂瀹氱悊 BC骞虫柟+AC骞虫柟=AB骞虫柟 BC骞虫柟+80*80=100*100 BC=60锛屽悓鐞咲C=60锛孊D=120绫=0.12鍗冪背 褰卞搷鏃堕棿0.12/18*3600=24绉 ...
绛旓細鎵浠ヨABD+瑙払AD=90搴 鎵浠ヨBAD+瑙扖AD=90搴 鎵浠ヨ涓夎琛屼负鐩磋涓夎褰 3.涓夎褰笁涓唴瑙掑害鏁扮殑姣旀槸1锛2锛3锛屽畠鐨勬渶澶ц竟涓簃锛岄偅涔堝畠鐨勬渶灏忚竟鏄灏戯紵鏍规嵁姝ｅ鸡瀹氱悊寰:鏈灏忚竟涓0.5m 4.鏂滆竟涓婄殑楂樹负m鐨勭瓑鑵扮洿瑙掍笁瑙掑舰鐨勯潰绉瓑浜庝粈涔堬紵瑙"姹傚嚭搴曡竟闀夸负2m,S=0.5*m*2m=m*m ...
绛旓細瑙ｉ鎬濊矾锛氱敱浜庢瀛愰潬鍦ㄥ涓婃椂灏变笌鍦伴潰涓庡褰㈡垚浜嗕竴涓洿瑙掍笁瑙掑舰锛岄涓凡鐭ヨ繖涓笁瑙掑舰鐨勬枩杈归暱涓庝竴鏉＄洿瑙掕竟闀匡紝寰堢畝鍗曞氨姹傚嚭鍙︿竴鏉＄洿瑙掕竟锛屼负24.褰撴瀛愬悜涓嬫粦鍔ㄦ椂锛屽師鏉ユ墍褰㈡垚鐨勭洿瑙掓槸涓嶅彉鐨勶紝鏂滆竟鏄笉鍙樼殑锛屽彧涓嶈繃鏄袱鏉＄洿瑙掕竟鏈夊彉鍖栥傞涓鏂滈潬鍦ㄥ涓婇《绔笅婊戜簡4绫筹紝灏辨槸鍒氬垰姹傚嚭鐨勯偅涓鏉＄洿瑙...
