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The perimeter of an isiosceles right-angled triangle is 4 cm. Find the length of the hypotenuse of the triangle.(leave the answer in surd form) 更新: √(2x2) = √2 x Help...I don't know why 更新 2: x = 4/(2 + √2) × (2 - √2)/(2 - √2) why!!!!!! × (2 - √2)/(2 - √2) 更新 3: 唉...我又唔明條題目,做唔到 A rectangular garden is 10 m wide and 30 m long. It is surrounded by a path of uniform width. If the area of the path is 176 m^2, find the width of the path. 更新 4: Sharon deposits $500000 in a bank at the beginning of 2009 for two years. The interest is calculated once a year as follows: 更新 5: The bank pays interest at r% p.a. for the first year. If the amount received at the end of the first year is deposited in the bank for another year,the bank pays interest at (r+1)% p.a. for the second year. If Sharon receives $25300 of the interest at the end of 2010,find value of r.

最佳解答:

圖片參考：https://s.yimg.com/lo/api/res/1.2/ZQit8r6YM3UMER1bF6V.OQ--/YXBwaWQ9dHdhbnN3ZXJzO3E9ODU-/http://i.imgur.com/ZH9B85L.gif Let x cm be the side of the isosceles right-angled triangle. Then, by Pythagoras theorem, the hypotenuse is √(x2 + x2) = √(2x2) = √2 x cm Therefore, the perimeter of the triangle is x + x + √2 x = (1 + 1 + √2)x = (2 + √2)x (cm) Consider (2 + √2)x = 4 x = 4/(2 + √2) x = 4/(2 + √2) × (2 - √2)/(2 - √2) x = 4(2 - √2)/(4 - 2) x = 4(2 - √2)/2 x = 2(2 - √2) x = 4 - 2√2 The length of the hypotenuse of the triangle is √2 x = √2 (4 - 2√2) = (4√2 - 4) cm 圖片參考：https://s.yimg.com/rk/HA00430218/o/1610793754.jpg 2014-09-14 17:42:17 補充： 這樣看吧： √(2x2) = √2√(x2) = √2 x 2014-09-14 19:02:10 補充： 補充發問： why!!!!!! × (2 - √2)/(2 - √2) 補充回答： 由於你見到分母有 (2 + √2) 這個項目。 我們為了方便計算，要做一個叫 rationalization of denomination （分母有理化）的步驟。 因此，要分子分母都乘 (2 - √2)，再計算。 至於為什麼要乘 (2 - √2) 呢？ 那是因為你見到有 (2 + √2)，那麼如果你乘了 (2 - √2) 就可得 4 - 2 = 2，沒有根號 (surd) 了。 背後用的原理是： (a + b)(a - b) ≡ a2 - b2 2014-09-14 19:04:47 補充： 問： A rectangular garden is 10 m wide and 30 m long. It is surrounded by a path of uniform width. If the area of the path is 176 m2, find the width of the path. 答： Let the width be x m. (30 + 2x)(10 + 2x) - (30)(10) = 176 2(15 + x)2(5 + x) - 300 = 176 4(15 + x)(5 + x) = 476 2014-09-14 19:05:30 補充： (15 + x)(5 + x) = 119 x2 + 20x + 75 = 119 x2 + 20x - 44 = 0 (x + 22)(x - 2) = 0 x = 2 or x = -22 (rejected) The width is 2 m. 2014-09-14 19:21:21 補充： 問： Sharon's deposit Question 答： 500000 × (1 + r%) × [1 + (r + 1)%] = 500000 + 25300 (1 + r/100) × [1 + (r + 1)/100] = 1.0506 (100 + r) × [100 + (r + 1)] = 10506 (100 + r)(101 + r) = 10506 10100 + 201r + r2 = 10506 r2 + 201r - 406 = 0 (r + 203)(r - 2) = 0 r = 2 or r = -203 (rejected)

其他解答:

ASK YOUR TEACHER!!!!!!!!!!|||||√(2x2) = √2 x Help...I don't know why 因為二次方只屬於x而不屬於2 若果平方共同擁有 那該是 √(2x)2 此外, x的平方再加平方根是變為x 由於2沒有平方 所以它依舊也擁有平方根0D7DAC4E6DF60DFA

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