A chessboard is made up of 8 rows and 8 columns of squares. Each little square is 42 \( \mathrm{~cm}^{2} \) in area. Show that the shortest distance from the upper right corner to the lower left corner of the chessboard is 73.32 cm .

A ladder is standing vertically, hard up against a wall. Omer comes and drags the foot of the ladder out 4 metres from the base of the wall. While doing so, he notices the top of the ladder slips down the wall a distance equal to \( 1 / 5 \) of its length. How long is the ladder?

Задание NO I (1 балл) Векторы \( \vec{a} \) и \( \vec{b} \) коллинеарны. Коллинеарны ли векторы: 1. \( \vec{a} \) и \( -3 \vec{b} \); 2. \( 4 \vec{a}-\vec{b} \) и \( \vec{b} \) ? Ответ поясните.

Calculate the size of the smallest angle of the trangle which has sider given by the equetions \( x+y=6 \), \( 2 y=x \) and \( 2 x-5 y=2 \).

A two-kilometre \( (2 \mathrm{~km}) \) pler and a one-kilometre \( (1 \mathrm{~km}) \) pler extend perpendlcularly into the ocean with four kilometres \( (4 \mathrm{~km}) \) offshore between the two plers. A swimmer wishes to swim from the end of the longer pier to the end of the shorter pler with one rest stop on the beach. Assuming that the swimmer recalls that, in any right-angled triangle, Hypotenese Find the shortest possible length of the swim and the location of the rest stop (land distance from the longer pier).

2. A farmer has a piece of land measuring 840 m by 396 m . He divides it into square plot equal size. Find the maximum area of one plot.