Question

три стороны описанного около окружности четырёхугольника относятся( в последовательном порядке) как 1:2 :7 Найдите большую из сторон этого четырёхугольника если его периметр равен 112

Answer 1

три стороны описанного около окружности четырёхугольника относятся( в последовательном порядке) как 1:2 :7 Найдите большую из сторон этого четырёхугольника если его периметр равен 112

Answer 2

Solution for Finding the Largest Side of the Quadrilateral

To find the largest side of the quadrilateral, we can use the given information about the ratios of the sides and the perimeter of the quadrilateral.

Given Information

The given ratios of the sides of the quadrilateral are 1:2:7 in sequential order. The perimeter of the quadrilateral is 112.

Calculating the Lengths of the Sides

To calculate the lengths of the sides, we can use the fact that the perimeter of a quadrilateral is the sum of all its sides.

Let's denote the lengths of the sides as x, 2x, 7x, and y, where y is the largest side.

According to the given information, the sum of the ratios is 1 + 2 + 7 = 10. Therefore, the total length of the sides is 10x.

Given that the perimeter of the quadrilateral is 112, we can set up the equation: x + 2x + 7x + y = 112 Solving for x: 10x + y = 112 y = 112 - 10x

Finding the Largest Side

To find the largest side, we need to maximize the value of y. This occurs when x is minimized.

To minimize x, we can consider the extreme case where x is as small as possible, which is when x = 1.

Substituting x = 1 into the equation for y: y = 112 - 10(1) y = 112 - 10 y = 102

Therefore, the largest side of the quadrilateral is 102.

Conclusion

The largest side of the quadrilateral, given the ratios of the sides and the perimeter, is 102.