How many scalene triangles with integral sides have a perimeter of 20cm?

3 scalene triangles with integral sides can have perimeter of 20 cm. Hope it helps you.

How do you find the area and perimeter of a scalene triangle?

What is the area and perimeter of scalene triangle? Area of scalene triangle is equal to half of the product of its base-length and height. Perimeter is equal to the sum of its three unequal sides.

What is the number of distinct triangles with integral valued sides and perimeter 14?

Therefore, the number of possible distinct triangles will be 4 with integral valued sides and perimeter 14. Note: Perimeter of a triangle is the outline length, i.e., the sum of all the sides of the triangle.

How do you find the perimeter of a scalene triangle?

The perimeter of a scalene triangle is equal to the sum of the length of sides of a triangle and it is given as, Perimeter = a + b + c units where a, b, and c are the lengths of the sides. For example, Look at the below image of a scalene triangle where the sides are a = 6 units, b = 15 units, and c = 20 units.

What is the area of the scalene triangle?

The area of the scalene triangle can be calculated using different formulas, Using base and height: (1/2) × base × height. Using Heron’s formula: √s(s−a)(s−b)(s−c) s ( s − a ) ( s − b ) ( s − c ) , where where a, b, c are the sides and s is the semi-perimeter, s = (a + b + c)/2.

What are the characteristics of a scalene triangle?

Scalene triangles must have unique side lengths (no two sides can be the same length), so it must have a side that is longer than the other two (the longest side). The other two sides also must not be the same, so one has to be longer than the other (we can call the longer side a and the shorter side b)

What makes a triangle degenerate?

Triangles are degenerate if the longest side is the same length as the sum of the other two sides. This basically forms a straight line. Scalene triangles must have unique side lengths (no two sides can be the same length), so it must have a side that is longer than the other two (the longest side ).

What is the length of the longest side of a triangle?

As such, the longest side must be less than half of the perimeter. The perimeter is 18 cm, so the longest side must be less than 18 cm 2 = 9 cm. The longest side can’t be 1 cm, as if it was, the rest of the triangle must have a perimeter of 18 − 1 = 17 cm.

What is the sum of the sides of a triangle?

Since triangles are scalene, all sides are of different lengths. Each side is of length 2 or more, and the sum of all sides is 12 or less. However, to be a triangle, the sum of the 2 shorter side lengths must be greater than the length of the longest side. This leaves: