Question

Write a general rule to find the perimeter of
(a) An isosceles triangle
(b) A scalene triangle

Answer 1

Hint:When we are asked to write the general rule of the perimeter, then we should at least know the concepts of the perimeter which is, the total length of the outline of the shape. For a triangle, it is the sum of the length of all the sides.

Complete step-by-step answer:
a) An isosceles triangle
Now, we know that an isosceles triangle is a triangle that has a length of two out of three sides equal. Let us consider a triangle ABC which is isosceles in shape that is two of its sides are equal in length. Let AB = AC = x and BC = y.

Now, we know that the perimeter of a triangle is the sum of the length of all the sides of the triangle. Mathematically, we can write it as,
Perimeter of the triangle = AB + AC + BC
Now, we assumed that AB = x = AC and BC =y. Therefore, we can write the perimeter of the triangle as
Perimeter of triangle = x + x + y
Perimeter of triangle = 2x + y
In other words, we can say that the perimeter of an isosceles triangle is the sum of twice the length of the equal sides and the third side.

(b) A scalene triangle
Now, we know that the scalene triangle is a triangle which has all sides of unequal length. Let us consider a triangle ABC, which is scalene in shape, that is, all of its sides are of unequal length. Let AB = x, BC = y and AC = z.

Now, we know that the perimeter of a triangle is the sum of the lengths of all the sides of the triangle. Mathematically, we can write it as,
Perimeter of triangle = AB + BC + AC
Now, we assumed that AB = x, BC = y and AC = z. Therefore, we can write the perimeter of the triangle as
Perimeter of triangle = x + y + z

Note: We know that the scalene triangle has all the sides of unequal length, but isosceles has 2 sides of equal length. So, we can calculate the perimeter of the isosceles triangle from the formula of the perimeter of the scalene triangle, but we cannot calculate the perimeter of the scalene triangle from the formula of the isosceles triangle.