Question

How do you find the perimeter of a triangle in which the sides measure \[2\sqrt 7 \], \[6\sqrt 7 \], \[4\sqrt 7 \]?

Answer 1

Hint: Here in this question, we have to find the perimeter of a triangle of the given sides measure. As we know the perimeter of the triangle is the sum of all 3 sides measures means adding of all the given 3 sides measures and further simplifying using the properties of radical addition to get the required perimeter of the triangle.

Complete step by step solution:
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 a triangle \[\Delta \,ABC\]

Whose length of base of the triangle is\[BC = 4\sqrt 7 \]
And the length of the other two lines of \[\Delta \,ABC\] is \[AB = 2\sqrt 7 \] and \[AC = 6\sqrt 7 \]
Perimeter of \[\Delta \,ABC\] is
\[ \Rightarrow \,\,P = 2\sqrt 7 + 4\sqrt 7 + 6\sqrt 7 \]
In order to add or subtract radicals, we must have "like radicals" that is the radicands and the index must be the same for each term. The radicand is the number inside the radical.
Radicals that are "like radicals" can be added or subtracted by adding or subtracting the coefficients.
\[ \Rightarrow \,\,P = \left( {2 + 4 + 6} \right)\sqrt 7 \]
On simplification, we get
\[ \Rightarrow \,\,P = 12\sqrt 7 \]
Or
\[ \Rightarrow \,P = 31.749\]

Hence, the perimeter of the of a triangle in which the sides measure \[2\sqrt 7 \], \[6\sqrt 7 \], \[4\sqrt 7 \] is \[12\sqrt 7 \] \[ \approx 31.749\].

Note: While determining the perimeter we use the formula. The unit for the perimeter will be the same as the unit of the length of a side or triangle. Whereas the unit for the area will be the square of the unit of the length of a triangle. We should not forget to write the unit. we should also know about the formula of a perimeter.