救下我呀~ 數學唔明r~~ 急

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2010-04-29 7:31 pm

(1) If the base of a triangle is increased by 10%, then by how much the percentage of the height must be decreased, in order to get the same area as before ?

(2) 50 kg of alloy steel contains 80% of iron and 20% of aluminum by weight. How much of aluminum to be melted so that the new alloy contains 32% of aluminum by weight?

求詳細解釋~

更新1:

我知道第2條~ 條式係咁~~ 2 let x be mass of aluminum to be melt (50*20%)+x=(50+x)*32% 10+x=16+0.32x 0.68x=6 x=8.82 (3 Significant Digits ) 但都係完全唔明 WHY 要咁計~

回答 (1)

用戶2053

2010-04-29 7:58 pm

✔ 最佳答案

1)Let x% of the height must be decreased :
Let h be the original height , b be the original base :
then the area of the original △
= bh/2
If the base of a triangle is increased by 10% , the height must be decreased
x% to get the same area , then
b(1 + 10%) * h(1 - x%) / 2 = bh/2
1.1(1 - x%) bh / 2 = bh / 2
1.1(1 - x%) = 1
1 - x% = 1 / 1.1
x% = 1 - 1/1.1 = 1/11 = 9.0909....%
The height must be decreased 9.0909....%

2)
(50*20%)+x = (50+x)*32%
左 : 50*20% 是原本aluminum的kg , 加多 x kg 就係aluminum新的kg ,
右 : (50+x) 是新混合金的總重 , 而裡面有32%係aluminum, 所以
(50+x)*32% 就係aluminum新的kg 。
兩者相等。

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