Question

From 20 cm diameter of circular piece,a rectangular piece with perimeter 28 cm ,find the dimension of rectangular .complete solution

Answer 1

Step-by-step explanation:

By the formula 2(a+b)=282(a+b)=28, a+b=14a+b=14, where the sides of the rectangle aa and bb. Since a,ba,b have to be positive, we can conclude that the maximum length of one side is smaller than 1414.

This length is smaller than 2020, the diameter of the circle, so any rectangle that can be possibly cut from the sheet.

As for translating the rectangle, we just have to translate the rectangle up or down until it touches the rectangle. Since there is a point where the rectangle transfers from being fully inside to partially outside, at one point the rectangle must touch the circle exactly.

Let there be a rectangle that is parallel to the xx-axis, and a circle centred at (0,0)(0,0). Then, we can find a chord, and thus a rectangle, that intersects the circle at two points (internally).

By some observation, the lines at the top and bottom of the rectangle have equations y=b2y=b2 and y=−b2y=−b2, where bbis the length of the chord, and also the top/bottom side of the rectangle.

Since you already have the yy-coordinates (because they lie on the line), we can use the equality y=b2y=b2 and put that value in the equation x2+y2=102x2+y2=102 with the two equations to solve for xx. This should give you the coordinates of the points you need.