5х +7х =180°
12х =180°
х = 15
5 × 15 =75
7 × 15 =105
@@@@@@@@@@@@@@@@@@@@@@@@@@
D=-9
a18=108
a1=a18-17d=108-17*(-9)=108+153=261
a2=261-9=252
a1=2
a2=9
d=9-2=7
S10=(2a1+9d)*10/2=(2*2+9*7)*5=(4+63)*5=67*5=335
a1=12
a2=6
d=6-12=-6
S20=(2a1+19d)*20/2=(2*12+19*(-6))*10=(24-114)*10=-90*10=-900
S=560 км
v₁- скорость первого
v₂- скорость второго
Запишем систему
<span>
![\left \{ {{t1=t2+1} \atop {v1=v2-10}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bt1%3Dt2%2B1%7D+%5Catop+%7Bv1%3Dv2-10%7D%7D+%5Cright.+)
</span>
![\left \{ {{ \frac{s}{v1} = \frac{s}{v2}-10 } \atop {v1=v2+10}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7B+%5Cfrac%7Bs%7D%7Bv1%7D+%3D+%5Cfrac%7Bs%7D%7Bv2%7D-10+%7D+%5Catop+%7Bv1%3Dv2%2B10%7D%7D+%5Cright.+)
Подставим во 2-е уравнение системы v₁=v₂+10
Получим:
![\frac{s}{v2+10}= \frac{s}{v2} -10](https://tex.z-dn.net/?f=+%5Cfrac%7Bs%7D%7Bv2%2B10%7D%3D+%5Cfrac%7Bs%7D%7Bv2%7D+-10+)
Домножив на
![v2(v2+10)](https://tex.z-dn.net/?f=v2%28v2%2B10%29)
получим:
![Sv2=s(v2+10)-10v2(v2+10)](https://tex.z-dn.net/?f=Sv2%3Ds%28v2%2B10%29-10v2%28v2%2B10%29)
![10s=10v2(v2+10)](https://tex.z-dn.net/?f=10s%3D10v2%28v2%2B10%29)
![s=v2(v2+10)](https://tex.z-dn.net/?f=s%3Dv2%28v2%2B10%29)
Подставив s=560 получим
![v2^{2} -10v2-560=0](https://tex.z-dn.net/?f=+v2%5E%7B2%7D+-10v2-560%3D0)
Откуда
![v2=5+3 \sqrt{65}](https://tex.z-dn.net/?f=v2%3D5%2B3+%5Csqrt%7B65%7D+)
и
![v1=15+3 \sqrt{65}](https://tex.z-dn.net/?f=v1%3D15%2B3+%5Csqrt%7B65%7D+)
Ответ:
![5+3 \sqrt{65}, 15+3 \sqrt{65}](https://tex.z-dn.net/?f=5%2B3+%5Csqrt%7B65%7D%2C+15%2B3+%5Csqrt%7B65%7D)
Длина большей диагонали 8 клеток