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Will the perimeter and the area of a triangle ever equal one another?
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.
Are two triangles with the same area and perimeter always congruent?
I believe so, though I am not sure I can prove it.
What are the properties of isosceles triangles?
All isosceles triangles: - Have angles that add up to 180 degrees - Have two equal sides. The unequal side is called the base. - Have equal base angles. - Have areas and perimeters that can be found using the formulas Area=1/2 X (base X height) and Perimeter=side+side+side An equilateral triangle with a right angle is called a right isosceles triangle. Also, all equilateral triangles are isoceles triangles, but not all isosceles triangles are right triangles.
Is area on a triangle larger than perimeter?
Perimeter is length (units feet, centimeters, etc.) Area is length2 (square feet, square centimeters etc.). But if you want to disregard the units, you can find triangles which perimeter is larger, smaller or even 'equal' to area, depending on scale.Take a 3,4,5 right triangle. The perimeter = 3+4+5= 12 units. Area = 3*4/2 = 6 square units. Now double the sides.Perimeter = 6 + 8+ 10 = 24 units. Area = 6*8/2 = 24 square units (the numbers are equal). Scaling it larger, then the valueof the area (in square units) will be larger than the perimeter value (in straight units).
What is the perimeter of a square that has an area of 81 meters square?
36, area is equal to length X width, perimeter is equal to 2(length)+2(width) in a square length is equal to width, so we take the square root of the area to find that both are 9, which means the perimeter is 9 X 4, 36.
