求求你們幫下我 math (盡量答)

2008-03-24 10:36 pm
1.直角三角形ABC,其中∠B=90°及AC=625cm。
若AB:BC=3:4,求△ABC的面積。

回答 (5)

2008-03-24 11:46 pm
✔ 最佳答案
1.直角三角形ABC,其中∠B=90°及AC=625cm。
若AB:BC=3:4,求△ABC的面積。

Answer:

Let AB = 3n, then BC = 4n
Use 畢式定理

AB x AB + BC x BC = 625 x 625 square cm

3n x 3n + 4n x 4n = 625 x 625

9n^2 + 16n^2 = 390625

25n^2 = 390625

n = 125 cm

Area of Triangle ABC = AB x BC

= 3n x 4n
= 3 x 125 x 4 x 125
= 187500 cm square



2008-03-24 14:43:00 補充

化簡下列各數式

2. 2√3×√21

Answer

2√3×√21

= 2√3×√3×√7
=2 x3×√7
=6√7

3. 3√8+√108-3√147
Answer:

3√8+√108-3√147
= 6√2 + 6√3 - 21√3
= 6√2 - 15√3

4. (2√2-33)(2√2+3√3)

Answer:
(2√2-33)(2√2+3√3)
= 8 + 6√6- 66√2 - 99√3

However, if question 4 is (2√2-3√3)(2√2+3√3)
then
(2√2-3√3)(2√2+3√3)
= 8 - 27
= - 19



2008-03-24 14:58:40 補充



5.一條長10m的竹竿倚在一堵直立的牆壁,它的頂端距離地面8m。若竹竿的頂端向下滑了2.5m,求竹竿底部所滑行的距離。

Answer:

竹竿的頂端向下滑了2.5m
thefore
竹竿的頂端在7.5m高
竹竿斜倚在牆, 長度 10m

根據畢氏定理,
Let 竹竿底部所滑行的距離 be x,

x^2 + 7.5 ^2 m square = 10^2 m square

x^2 = 100 - 56.25 = 44.75 m square = 175/4 m square

x = √175 / 2 m

2008-03-24 16:01:43 補充:
Sorry, the previous answer of question 5 is wrong

Answer:

竹竿的頂端在8 - 2.5m = 5.5m高
竹竿斜倚在牆, 長度 10m

根據畢氏定理,
Let 竹竿底部所滑行的距離 be x,

x^2 + 5.5 ^2 m square = 10^2 m square

x^2 = 100 - 30.25 = 69.75 m square = 279/4 m square

x = 3√31 / 2 m

2008-03-24 16:07:04 補充:
Sorry, the previous answer still wrong

Before sliding, Original base length be y

y^2 + 8^2 =10^2

y = 6

After Sliding

x^2 + 5.5^2 = 10^2

x = 3 √31 / 2

Sliding length = x - y

= 3 √31 / 2 - 6
= ( 3 √31 - 12 ) / 2
= 3 ( √31 - 4 ) / 2 m
2008-03-25 1:12 am
1.直角三角形ABC,其中∠B=90°及AC=625cm。
若AB:BC=3:4,求△ABC的面積。

2008-03-24 14:43:00 補充

化簡下列各數式

2. 2√3×√21

3. 3√8+√108-3√147

4. (2√2-33)(2√2+3√3)

2008-03-24 14:58:40 補充

畢式定理

5.一條長10m的竹竿倚在一堵直立的牆壁,它的頂端距離地面8m。若竹竿的頂端向下滑了2.5m,求竹竿底部所滑行的距離。

6.在一個水池離岸邊2m處有一棵植物AB它露出水面的部分長1m。若把它的頂端A牽引到岸邊C,則頂端A剛好與水面相齊。求
(a)該水池的深度
(b)該棵植物的高度
2008-03-24 11:16 pm
ab:bc=3:4
bc=5(pythagories theorem)
ab=3/5x625= 375
bc=4/5x625=500
the area =375x500/2=93750cm2
5. the length = square root of (8^2-5.5^2)
= 5.8m
2008-03-24 10:55 pm
試答如下:

1. 根據畢氏定理,AB=15,BC=20,所以△ABC的面積是150。

2. = 2√3 x √3 x √7 = 6√7

3. = 3√2 x √2 x √2 + √2 x √2 x √27 - 3√3 x √7 x √7
= 6√2 + 6√3 - 21√3
= 6√2 - 15√3

4. = 8 + 6√2√3 - 66√2 - 99√3
2008-03-24 10:54 pm
1. ∠B=90°

ab^2+bc^2=ac^2(p.s:ac一定係斜邊)(畢氏定理)

3x^2+4x^2=625^2

7x^2=390625

x=236.2277956..........................

ab=3x=3乘236.2277956..........................=自己計

bc=4x=4乘236.2277956..........................=自己計

area=3x乘4x除2=12x^2/2=自己計

圖:http://img151.imageshack.us/my.php?image=rw1gc4.png

2008-03-24 15:02:49 補充:
畢氏定理:眾所周知,畢氏定理是指直角三角形的斜邊(hypotenuse)的平方 等於另外兩邊的平方之和,這種超過三百多種証明方法的定理.

a^2+b^2=c^2


下面的朋友:15^2+20^2=625,但不等於625^2....所以個條唔係畢氏定理.依據題目,我睇第一條已經錯左

2008-03-24 15:31:41 補充:
更正:3x^2+4x^2=625^2


9x^2+16x^2=390625

X=125

ab=375

BC=500

area=375 X 500 /2 =93750CM^2

2008-03-24 15:38:33 補充:
http://img175.imageshack.us/my.php?image=88471998tt4.png(第5題)

2008-03-24 15:41:49 補充:
3x^2+4x^2=625^2

7x^2=390625

x=236.2277956..........................

ab=3x=3乘236.2277956..........................=自己計

bc=4x=4乘236.2277956..........................=自己計

area=3x乘4x除2=12x^2/2=自己計
上為錯誤,下為更正

(3x)^2+(4X)^2=390625

X=125

AREA3X X 4X /2=3(125) x 4(125)/2=93750XM^2
參考: 自己


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