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Will the perimeter and the area of a triangle ever equal one another?
Wiki User
∙ 15y ago
Consider any triangle with given angles. If you expand it by a linear scale factor x, then its perimeter is multiplied by x, and its area by x2. When x is big, x2 is bigger than x. The area thus grows relative to the perimeter; as x tends to infinity, the ratio area/perimeter (call it R) tends to infinity. When x is small, x2 is smaller than x. The area thus shrinks relative to the perimeter; as x tends to zero, the ratio R tends to zero. For perimeter to equal area, R must equal 1. Since R is continuously defined, and (as we have just seen) it varies between zero and infinity, there must be some value of x that renders R = 1. This proves that an infinite number of triangles have perimeter equal to area, since our reasoning applied to triangles of any shape. To give one example, we'll find the equilateral triangle with perimeter equal to area. Set the length of a side equal to 2y. area = height x base / 2 = y2sqrt3 perimeter = 6y So, solve 6y = y2sqrt3 6 = ysqrt3 y = 6/sqrt3 = 2sqrt3 One more trivial example: if perimeter equals zero, then it definitely equals area.
Wiki User
∙ 15y ago
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What is the perimeter of a triangle that has a area of 6.5 cm?
The minimum perimeter is when the triangle is an equilateral triangle. The perimeter of any other triangle with the same area will be longer. In the case of an equilateral triangle area = (√3)/4 × side² → side = √(4×6.5 cm²/√3) → perimeter = 3 × side = 3 × √(4×6.5 cm²/√3) ≈ 11.62 cm → The triangle has a perimeter greater than or equal to approx 11.62 cm.
What is the area of an equilateral triangle that has a perimeter of 71 feet?
Find the area of an equilateral triangle if its perimeter is 18 ft
One of two numbers that can be both the area and perimeter of a triangle whose side lengths are a pythagorean triple?
For the 6:8:10 triangle, area = perimeter = 24. Also, for the 5:12:13 triangle, area = perimeter = 30. Whether these are indeed the only examples I am not sure. That would take some proving.
One of 2 numbers that can be both the area and perimeter of a triangle whose side lengths are a Pythagorean triple?
For the 6:8:10 triangle, area = perimeter = 24. Also, for the 5:12:13 triangle, area = perimeter = 30. Whether these are indeed the only examples I am not sure. That would take some proving.
Find the area of an equilateral triangle that has a perimeter of 21 inches Round the answer to one decimal place?
Find the area of an equilateral triangle that has a perimeter of 21 inches. Round the answer to one decimal place.
Sides of traingle giving equal permeter and area?
I am assuming that "traingle" is meant to be triangle and "permeter" is meant to be perimeter.The area of a triangle cannot be equal to its perimeter because the area is a measure in 2-dimensional space whereas a perimeter is a 1-dimensional measure. So their dimensions will always be different.Furthermore, the area of a triangle is not determined by its perimeter. The area of a triangle can be changed - without affecting its perimeter - simply by changing the angles.
What is the perimeter of a triangle that has a area of 6.5 cm?
The minimum perimeter is when the triangle is an equilateral triangle. The perimeter of any other triangle with the same area will be longer. In the case of an equilateral triangle area = (√3)/4 × side² → side = √(4×6.5 cm²/√3) → perimeter = 3 × side = 3 × √(4×6.5 cm²/√3) ≈ 11.62 cm → The triangle has a perimeter greater than or equal to approx 11.62 cm.
What is equal to the area of an equilateral triangle whose perimeter is 36 inches?
62.354 inches2
What is the area of a triangle that has a perimeter of 37?
The perimeter of a triangle does not provide sufficient information to calculate its area.
What s the perimeter of an equilateral triangle whose area in square cm is equal to the square root of 3?
The perimeter is 6 cm.
What is the relation between perimeter and triangle area?
If you double (2 times) the perimeter the area will will be 4 times larger. Therefore the area is proportional to the square of the perimeter or the perimeter is proportional to the square root of area. The relationship as shown above applies only to triangles with similar proportions, that is when you scale up or down any triangle of fixed proportions. Other than that requirement, there is no relationship between perimeter and area of any shape of triangle except that it can be stated that the area will be maximum when the sides are of equal length (sides = 1/3 of perimeter).
How do you get the area of the triangle from perimeter?
From only the perimeter you cannot.
The area of a given hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches Find the length of a side of the regular hexagon?
The area of a given hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches. Find the length of a side of the regular hexagon.Click once to select an item at the bottom of the problem.
How do you find the perimeter of a triangle if you know the area?
You cannot. For a given area, an equilateral triangle will have the smallest perimeter but that perimeter can be increased - without limit - without increasing the area.
How do you find the perimeter of a right angled triangle using the area?
how to find the perimeter of a right angled triangle using the area
How do you find the perieter and area of a triangle?
The perimeter of an object is simply the length of its border, so the perimeter of a triangle is the sum of the lengths of its 3 sides.The area of a triangle is equal to half of its base times its height, for example if a triangle had a base of length 4 and was 5 units tall, it would have an area of (4*5)/2, or 10 units2.
What is the area of an equilateral triangle that has a perimeter of 71 feet?
Find the area of an equilateral triangle if its perimeter is 18 ft
