300ad ds

白露丹枫 · 发表于 2019-11-15 20:21:47

If the lengths of the legs of a right triangle are integers, what is the area of the triangular region?

(1)The length of one leg is 3/4 the length of the other.

(2)The length of the hypotenuse is 5.

<2>为什么可以
我按照5,12,13 或者9 40 41 比例配出来5

What is the length of the hypotenuse of △ABC?

(1)The lengths of the three sides of △ABC are consecutive even integers .

(2)The hypotenuse of △ABC is 4 units longer than the shorter leg.

这个2 为什么又不行

橙子酱 · 发表于 2019-11-15 20:30:32

第一个说了直角边都是整数，第二个没说

白露丹枫 · 发表于 2019-11-15 21:18:59

那单独看第二题的2为啥不行呢 6 8 10？

Parker_1997 · 发表于 2019-11-15 22:38:42

Let's denote three sides by x,y,z. (z stands for hypotenuse)

Question: whether xy is solved uniquely

(1) x=3a  y=4a  xy=12a^2 the value of xy depends on a

(2) x^2+y^2 = 25  where x, y are integers. Notice that x and y share the same position, we can simply let x<=y<5 and it does not affect the value of xy .

x=1 , y_max = 4,  x^2+y^2 = 17  Not satisfied.

x=2, y_max =4 Not satisfied.

x=3,y_max= 4 Bravo.

x=4, y_max = 4  Not satisfied. (As I mentioned above, the case x=3,y=4 and another case x=4, y=3 can be viewed as the same thing because of the same position of x and y, therefore, the value of xy does not change.)

Under Statement 2, we have unique value of xy, which is 12.

大王oli · 发表于 2019-11-17 19:43:24

求楼主分享300难题数学部分的题

感激不尽！

白露丹枫 · 发表于 2019-11-26 09:07:34

可以在gmatla做，CD 的怎么说有必出老师的网

300ad ds

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