Question

In the figure, is a parallelogram in which \[KN = 8\], \[KP = 6\], \[NP = 4\], find the perimeter of \[\vartriangle MPL\]

Answer 1

Hint: Here in this question, we have to find the perimeter of a triangle \[\vartriangle MPL\] within the given parallelogram . As we know the perimeter of the triangle is the sum of all 3 sides measures. First we have to know the length of each side of the triangle by using a parallelogram. Later by adding length of all sides of \[\vartriangle MPL\] we get the required result.

Complete step by step solution:
In geometry, perimeter can be defined as the path or the boundary that surrounds a shape. It can
also be defined as the length of the outline of a shape.
Finding the perimeter of a triangle means finding the distance around the triangle. The simplest way to find the perimeter of a triangle is to add up the length of all of its sides
The perimeter of the triangle with sides a, b and c is \[p = a + b + c\].
Consider the question,
Given, parallelogram having a measurement of \[KN = 8\], \[KP = 6\] and \[NP = 4\].

We have to find the perimeter of the triangle \[\vartriangle MPL\].
As by the properties of parallelogram: In any parallelogram the parallel or opposite sides are equal and its diagonals are bisect each other.
Then, In
\[KN = ML = 8\], \[KP = MP = 6\] and \[NP = PL = 4\].
Now, consider a triangle \[\vartriangle MPL\] which lies within the parallelogram

Perimeter of \[\vartriangle MPL\] is
\[ \Rightarrow Perimeter = PL + MP + ML\]
\[ \Rightarrow Perimeter = 4 + 6 + 8\]
\[\therefore Perimeter = 18\]units
Hence, the perimeter of the triangle \[\vartriangle MPL\] is 18 units.
So, the correct answer is “18 units. ”.

Note: Remember the parallelogram is a one of the types of quadrilateral, which has some basic properties like the opposite or parallel sides and the opposite angles are always equal and their diagonals are bisected. While doing measurement based problems, do not forget to write the unit with the final answer, the unit for the perimeter will be the same as the unit of the length of a side or polygon.