1.
AD = 3 , FE = 1
BC + 3 = 2(1+3) = 8
BC = 5
梯形的高 = △GFE的高 * (3+5)/1 = 8
梯形面積/△GFE = (3+5)*8 /1 = 64
2.
設BP = x
x² + 2² = (6-x)² = x² - 12x + 36
12x = 32
x = 8/3
3.
設∠BCD = x
x + ∠ABC = ∠ADC = ∠ACD = ∠ACB -x
2x = ∠ACB - ∠ABC = 38
x = 19
4.
高 = √21，周長 = 14
設底長 2x
腰長 = (14 - 2x)/2 = 7-x
(7-x)² = x² + (√21)²
x² - 14x + 49 = x² + 21
14x = 28
x = 2
面積 = 2√21
5.
a² + 9² = (20b+1)²
a² + 81 = 400b² + 40b + 1
a² = 400b² + 40b - 80 = 40(10b²+b-2)
b 是正整數，所以 a² 是 40 的倍數
其實，40 =2² * 2 * 5 ，a 是正整數 (至少還能再補個 2*5)
a² 也會是 40 * 10 = 400 的倍數 |
