В выпуклом шестиугольнике четыре стороны равны, пятая сторона на 15 мм меньше перввой, а шестая - в 3 раза больше второй. Найдите стороны шестиугольника, если его периметр равен 121 мм. 1) 16 мм; 16 мм; 16 мм; 16 мм; 1 мм; 48 мм 2) 16 мм; 16 мм; 16 мм; 1 мм; 1 мм; 50 мм 3) 17 мм; 17 мм; 17 мм;; 17 мм; 2 мм; 51 мм 4) 17 мм; 17 мм; 17 мм; 2 мм; 2 мм; 51 мм

To solve the problem, we can set up an equation using the given information and use algebra to find the unknown sides of the hexagon.

Let's assume the length of the four equal sides is x mm.

According to the problem, the fifth side is 15 mm less than the first side, so its length is x - 15 mm.

The sixth side is three times the length of the second side, so its length is 3x mm.

The perimeter of the hexagon is 121 mm, so we can set up the equation as follows:

x + x + x + x + (x - 15) + 3x = 121

Combining like terms, we get:

7x - 15 = 121

Adding 15 to both sides, we have:

7x = 136

Dividing both sides by 7, we find:

x = 19.43

Since x represents the length of the equal sides, which must be a whole number, we can round the value of x to the nearest whole number. So x is approximately 19 mm.

Using this value, we can find the lengths of all sides of the hexagon:

First side: x = 19 mm Second side: x = 19 mm Third side: x = 19 mm Fourth side: x = 19 mm Fifth side: x - 15 = 19 - 15 = 4 mm Sixth side: 3x = 3 * 19 = 57 mm

Therefore, the correct answer is option 4) 17 mm; 17 mm; 17 mm; 2 mm; 2 mm; 51 mm.