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little tina 發問時間: 科學數學 · 9 年前

一題三角型的面積問題,一題數學分數問題

Q1: In the figures above, if the area of the trangle on the right is twice the area of the triangle on the left, then In term of s, S=?

答案是:根號2 s

因為我不知道這裡如何畫圖,所以我用敘述的

右邊三角型比左邊三角型大,右邊三角型的底為大S,做左邊三角型的底為小s。

兩個三角型最上面為y度,右邊是z度,左邊是x度。三角型的樣子類似正三角型。

我自己帶數字去算為:S=2s →我想破頭~~都算不出來

Q2:Alice's take-home pay last year was the same each month, and she saved the dame fraction of her take-home pay each month. The total amount of money that she had saved at end of year was 3 times the amount of that portion her monthly take-home pay that she did not save. If all the moeny that she saved last year was from take-home pay. what fration of her take-home pay did she save each month?

答案:1/5 (take-home pay →實得薪水)

我是算3/4,我後來帶數字,進去算也是3/4 ~~~想不透為什麼是1/5

請高手幫忙謝謝~~~

1 個解答

評分
  • 浮雲
    Lv 5
    9 年前
    最佳解答

    第一題

    沒有圖只好用想像的

    按照你的說法,這兩個三角形大小不同但各相對應的角度相同,因此這兩個三角形為相似形

    根據相似形的定義,各相對應邊長度呈等比例

    假設S為s的 X倍, 則高H也是h的X倍(X>0)

    大三角面積=1/2 SH= 2x小三角面積=2x 1/2 sh

    SH=(Xs)(Xh)=2x sh---> X^2sh=2sh---> X^2=2

    X=根號2

    第二題

    假設每月薪水為Y元,其中儲蓄的比例為X(X,Y不等於零)

    依題意

    12XY=3Y(1-X)---> 12XY=3Y-3XY--->15XY=3Y

    15X=3---> X=1/5

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