一本课外书一共有120页，看了全部的 $\frac{4}{5}$ ，已经看了105页．

为在池塘两侧的A，B两处架桥，要想测量A，B两点的距离，如图所示，找一处看得见A，B的点P，连接AP并延长到D，使PA=PD，连接BP并延长到C，使．测得CD=35m，就确定了AB也是35m，说明其中的理由；

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Characters: Peppa, George, Mummy Pig, Daddy Pig

Setting: Mummy Pig is working on her computer. Daddy Pig is making soup for lunch.

Peppa: Daddy? Can we go and watch mummy on her computer?

Daddy Pig: Yes, as long as you don't disturb her. She has a lot of important work to do today.

Peppa: Thank you, Daddy!

Peppa: (Peppa and George run into mummy's room.) Mummy. Can George and I sit on your legs and watch you work?

Mummy Pig: Yes, if you both sit quietly.

Peppa: (Peppa and George watch mummy work on the computer for a while.) Mummy? Can we play that computer game Happy Mrs. Chicken?

Mummy Pig: We can play Happy Mrs. Chicken later. But now I have to work.

Peppa: Mummy? Can we help you work?

Mummy Pig: No, Peppa! You mustn't touch the computer. And George, you mustn't touch the computer, either.

Peppa: Yes, George. You mustn't do this (Peppa began to knock on the keyboard).

Mummy Pig: Peppa, stop!

Peppa: Sorry, Mummy. I was just showing George what not to do.

Mummy Pig: Oh, dear. The computer doesn't work!

已知正项等比数列$\left\{a_n\right\}$满足：$a_7=a_6+2a_5$，若存在两项$a_{m,}{a}_n$使得$\sqrt{a_m{a}_n}=4a_1$则$\frac{1}{m}+\frac{4}{n}$的最小值为（    ）．