Question

What is the perimeter of a triangle with sides \[1\dfrac{3}{5},3\dfrac{1}{5}\] and \[3\dfrac{3}{5}\]?

Answer 1

Hint: From the definition of the perimeter we know, the perimeter of a triangle, \[P = a + b + c\] units
Where
“a” ,”b” ,”c” are the sides of the triangle.
We will put the length of the sides of the triangle in the above formula then solving it we will get the expression for the perimeter.

Complete step-by-step solution:
It is given that; the sides of the triangle are \[1\dfrac{3}{5},3\dfrac{1}{5}and3\dfrac{3}{5}\].
We need to find out the perimeter of the triangle.
Since the perimeter is equal to the sum of all the sides of the polygon. Hence, in the case of a triangle, the perimeter (P) is;
\[P = \] Sum of all its four sides
\[\Rightarrow P = a + b + c\]
\[\Rightarrow P = 1\dfrac{3}{5} + 3\dfrac{1}{5} + 3\dfrac{3}{5}\]
\[\Rightarrow P = \dfrac{8}{5} + \dfrac{{16}}{5} + \dfrac{{18}}{5}\]
\[\Rightarrow P = \dfrac{8}{5} + \dfrac{{16}}{5} + \dfrac{{18}}{5}\]
\[\Rightarrow P = \dfrac{{8 + 16 + 18}}{5}\]
\[\Rightarrow P = \dfrac{{42}}{5} = 8\dfrac{2}{5}\]
Thus the perimeter of the triangle whose sides are \[1\dfrac{3}{5},3\dfrac{1}{5}and3\dfrac{3}{5}\] is \[8\dfrac{2}{5}\]units.

Note: A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted by triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane. (i.e. a two-dimensional Euclidean space). In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane.
The perimeter of a triangle is defined as the sum of all the sides of a triangle.
For any polygon, the perimeter formulas are the total distance around its sides. In case of a triangle, there are three sides. Thus, the perimeter will be the sum of the length of these three sides and it is denoted by the alphabet “P”.