4/9 и 1/6 4/9 = 8/18 и 1/6 = 3/18
9 = 3 * 3 6 = 2 * 3 НОК (9 и 6) = 9 * 2 = 18
1/6 и 2/15 1/6 = 5/30 и 2/15 = 4/30
6 = 2 * 3 15 = 3 * 5 НОК (6 и 15) = 2 * 3 * 5 = 30
5/12 и 7/16 5/12 = 20/48 и 7/16 = 21/48
12 = 2 * 2 * 3 16 = 2 * 2 * 2 * 2 НОК (12 и 16) = 16 * 3 = 48
3/4 и 5/18 3/4 = 27/36 и 5/18 = 10/36
4 = 2 * 2 18 = 2 * 3 * 3 НОК (4 и 18) = 4 * 9 = 36
3/10 и 7/15 3/10 = 9/30 и 7/15 = 14/15
10 = 2 * 5 15 = 3 * 5 НОК (10 и 15) = 2 * 3 * 5 = 30
5/18 и 7/24 5/18 = 20/72 и 7/24 = 21/72
18 = 2 * 3 * 3 24 = 2 * 2 * 2 * 3 НОК (18 и 24) = 8 * 9 = 72
11/30 и 7/24 44/120 и 35/120
30 = 2 * 3 * 5 24 = 2 * 2 * 2 * 3 НОК (30 и 24) = 8 * 3 * 5 = 120
9/34 и 8/51 9/34 = 27/102 и 8/51 = 16/102
34 = 2 * 17 51 = 3 * 17 НОК (34 и 51) = 2 * 3 * 17 = 102
у-длина огорода
ху=1500 =>х=1500/у
(х+5)(у-10)=1500
ху=(х+5)(у-10)
ху=ху-10х+5у-50
10х=5у-50 разделим на 5
2х=у-10
у=2х+10
у=2*1500/у+10
у=3000/у+10 домножим на у
у²=3000+10у
у²-10у-3000=0
D = (-10)2 - 4·1·(-3000) = 100 + 12000 = 12100
у1=(10 - √12100)/(2*1) = (10 - 110)/2 = -100/2 = -50 -не подходит
у2=(10 + √12100)/(2*1) = (10 +110)/2 =120/2 =60м- длина огорода
1500/60=150/6=75/3=25м-ширина огорода
25+5=30м-ширина сада
60-10=50м-длина сада
ответ: огород размером 60м на 25м, сад размером 50м на 30м
4/9 и 1/6 4/9 = 8/18 и 1/6 = 3/18
9 = 3 * 3 6 = 2 * 3 НОК (9 и 6) = 9 * 2 = 18
1/6 и 2/15 1/6 = 5/30 и 2/15 = 4/30
6 = 2 * 3 15 = 3 * 5 НОК (6 и 15) = 2 * 3 * 5 = 30
5/12 и 7/16 5/12 = 20/48 и 7/16 = 21/48
12 = 2 * 2 * 3 16 = 2 * 2 * 2 * 2 НОК (12 и 16) = 16 * 3 = 48
3/4 и 5/18 3/4 = 27/36 и 5/18 = 10/36
4 = 2 * 2 18 = 2 * 3 * 3 НОК (4 и 18) = 4 * 9 = 36
3/10 и 7/15 3/10 = 9/30 и 7/15 = 14/15
10 = 2 * 5 15 = 3 * 5 НОК (10 и 15) = 2 * 3 * 5 = 30
5/18 и 7/24 5/18 = 20/72 и 7/24 = 21/72
18 = 2 * 3 * 3 24 = 2 * 2 * 2 * 3 НОК (18 и 24) = 8 * 9 = 72
11/30 и 7/24 44/120 и 35/120
30 = 2 * 3 * 5 24 = 2 * 2 * 2 * 3 НОК (30 и 24) = 8 * 3 * 5 = 120
9/34 и 8/51 9/34 = 27/102 и 8/51 = 16/102
34 = 2 * 17 51 = 3 * 17 НОК (34 и 51) = 2 * 3 * 17 = 102