subject: Sum Of Triangle Sides [print this page] Introduction to sum of triangle sides: Introduction to sum of triangle sides:
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. In an equilateral triangle all sides have the same length. In an isosceles triangle, two sides are equal in length. In a scalene triangle, all sides are unequal.
Perimeter - Sum of three Sides of the Triangle:
The perimeter of a shape is out side distance of that shape. To find the perimeter of a shape, take the sum of the length of each side. In right triangle, the perimeter can be calculated by taking the sum of the three side length of triangle.
Formula to find perimeter:
Perimeter of the triangle = sum of three side length of triangle.
P= a + b + c.
Example problems:
1. The three sides of right triangles are 5cm, 6cm and 7 cm. find the perimeter of the triangle.
Solution:Given:
Three side length 5cm, 6cm and 7 cm.
Formula:Perimeter of the triangle = sum of three side length of triangle.
Perimeter of the right triangle (p) =a + b + c =5 + 6 + 7 =18
Perimeter of the right triangle (p) =18 cm
2. The three sides of right triangles are 7m, 9m and 11 m. find the perimeter of the triangle.
Solution:Given:
Three side length 7cm, 9cm and 11 cm.
Formula:Perimeter of the triangle = sum of three side length of triangle.
Perimeter of the right triangle (p) =a + b + c =7 + 9+ 11 =27
Perimeter of the right triangle (p) =27cm
3. The three sides of right triangles are 6.4cm; 5cm and 4 cm. find the perimeter of the triangle.
Solution:Given:
Three side length 6.4cm, 5cm and 4 cm.
Formula:Perimeter of the triangle = sum of three side length of triangle.
Perimeter of the right triangle (p) =a + b + c =6.4 + 5 + 4 = 15.4cm
Perimeter of the right triangle (p) =15.4cm
Practice Problem in Triangle:
1. Find the perimeter of the triangle, its sides length are 3 m, 6m and 10m.
Ans: 19m
2. Three sides of triangles are 12 feet, 14 feet and 18.4 feet. Find perimeter of triangle.
Ans: 44.4 feet
In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side (and, if the setting is a Euclidean space, then the inequality is strict if the triangle is non-degenerate).[1][2]
In Euclidean geometry and some other geometries the triangle inequality is a theorem about distances. In Euclidean geometry, for right triangles it is a consequence of the Pythagorean theorem, and for general triangles a consequence of the law of cosines, although it may be proven without these theorems. The inequality can be viewed intuitively in either R2 or R3. The figure at the right shows three examples beginning with clear inequality (top) and approaching equality (bottom). In the Euclidean case, equality occurs only if the triangle has a 180 angle and two 0 angles, making the three vertices collinear, as shown in the bottom example. Thus, in Euclidean geometry, the shortest distance between two points is a straight line.
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In spherical geometry, the shortest distance between two points is an arc of a great circle, but the triangle inequality holds provided the restriction is made that the distance between two points on a sphere is the length of a minor spherical line segment (that is, one with central angle in [0, p]) with those endpoints
