No triangle exists that minimizes that condition. However, the infinum of the perimeters of all such triangles = twice the distance from (a,b) to the line y = x. That's just an application of the triangle inequality after picking the first two points (one is on the line, the other is (a,b)) of any triangle.
The perimeter of an equilateral triangle exceeds the perimeter of a square by 1989cm. The length of each side of the triangle exceeds the length of each side of the square by d cm. The square has perimter greater than 0. How many positive integers are not possible values for d? t for side of...
A square S1 has a perimeter of 40 inches. The vertices of a second square S2 are the midpoints of the sides of S1. The vertices of a third square S3 are the midpoints the sides of S2. Assume the process continues indefinitely, with the vertices of S K+1 being the midpoints of the sides of Sk...
Show that the perimeter Pn of an n-sided regular polygon inscribed in a circle of radius r is P_{n}= 2n r \sin(\frac{\pi}{n}) Find the limit of Pn as n approaches ∞ My attempt: The sum of the interior angles is \pi (n-2) . If we apply the cosine law to find the length of each side of the...
Perimeter of a circle as a limit of inscribed regular sided polygon
To granddad Really sorry if i am getting back to you on this. For the first question perimeter of square , the data was the following: Upper bound perimeter=27.26cm Lower bound perimeter=27.22cm Give the perimeter of the square to an appropriate degree of accuracy As you said The true value of the perimeter lies between 27.22 cm and 27.26 cm.