I am not sure what you mean by a "fundamental" number (I've never heard of that term being used with reference to the numbers themselves); I guess you mean an "integer".
For a triangle to exist the shorter two sides must be longer than the longest side. Thus there is an upper limit to the length of the longest side of a triangle.
For a given perimeter, the longest side must be less than half the perimeter. For a perimeter of 42cm this means that the longest side is less than 42 cm ÷ 2 = 21 cm.
If we focus on the longest side of a triangle, as it becomes shorter, one or both of the other two sides must increase in length, they can equal but never be longer than this longest side. Thus there is also a lower limit below which the longest side cannot be; this is when all three sides are equal and the triangle is an equilateral triangle. For a perimeter of 42cm the longest side is greater than or equal to 42 cm ÷ 3 = 14 cm
So with a perimeter of 42 cm we have:
14 cm ≤ longest side < 21 cm
Which means for an integer length, the longest side can be 14 cm, 15 cm, 16 cm, 17 cm, 18 cm, 19 cm or 20 cm.
26
You mean the largest possible area with a perimeter of 18, right? Well, the largest area is with a circle, which has area 81/pi which is approximately 25.7831 If you need a rectangular area, the largest is a square of width=length (definition of square) = 4.5 This has area 4.52 which is 20.25, substantially less than the circles area...
The largest angle then will be 94.35 degrees opposite the longest sides of 162cm and by using the sine rule of 120/sin(94.35) = b/sinB = c/sinC the perimeter of the triangle works out as 381.83cm rounded to two decimal places.
There is no such thing as a three sided rectangle. They have four sides. Length and width of a rectangle being THE SAME (having a 1:1 ratio) will provide the largest area possible. In other words, for a given perimeter, a square is the largest rectangle. If you mean a triangle (which has three sides), then all sides being equal will still yield the largest area.
The smallest possible perimeter is 20-ft, but there is no largest possible perimeter.You can make it as large as you want, with no limit.Examples:5-ft x 5-ft . . . . area = 25 ft2 . . . perimeter = 20 ft2.5-ft x 10-ft . . area = 25 ft2 . . . perimeter = 25 ft1-ft x 25-ft . . . area = 25 ft2 . . . Perimeter = 52 ft6-in x 50-ft . . . area = 25 ft2 . . . Perimeter = 101 ft3-in x 100-ft . . area = 25 ft2 . . . perimeter = 2001/2 ft1-in x 300-ft . . area = 25 ft2 . . . perimeter = 6001/6 ft0.1-in x 3,000-ft . . area = 25 ft2 . . . perimeter = 6,0001/60 ft
The smallest perimeter is 4*sqrt(24) = approx 19.6 cm There is no largest perimeter.
26
90
Largest = 86, Smallest 26
It is 36 cm2
The smallest is just over 40 units. At 40 units it is no longer a rectangle but a square. There is no largest perimeter.
A right triangle is a triangle with one of its angles being 90o. The requirements for the other two angles are that they both be acute and total to 90o. Therefore, the largest possible acute angle in a right triangle is 89.99999...o.
For a given perimeter, the circle has the largest area possible.
You mean the largest possible area with a perimeter of 18, right? Well, the largest area is with a circle, which has area 81/pi which is approximately 25.7831 If you need a rectangular area, the largest is a square of width=length (definition of square) = 4.5 This has area 4.52 which is 20.25, substantially less than the circles area...
1800 square cm.
The largest angle then will be 94.35 degrees opposite the longest sides of 162cm and by using the sine rule of 120/sin(94.35) = b/sinB = c/sinC the perimeter of the triangle works out as 381.83cm rounded to two decimal places.
After the partition of Madhya Pradesh and Chhatisgarh, now Rajasthan is the largest perimeter State of India.