✔ 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