The perimeter of an isosceles triangle is greater than the perimeter of the equilateral triangle because the legs of an isosceles triangle with a 65 degree vertex angle are congruent with the sides of an equilateral triangle.
Given :
The legs of an isosceles triangle with a 65 degree vertex angle are congruent with the sides of an equilateral triangle.
The following steps can be used in order to determine which triangle has a greater perimeter:
Step 1 - According to the given data, the vertex angle is 65 degrees. So the base angle is 57.5 degrees.
Step 2 - The perimeter of the isosceles triangle is given by:
P = 3a
Step 3 - The perimeter of the equilateral triangle is given by:
P' = 2b + c
Step 4 - According to the given data, the legs of both triangles are congruent.
a = b
Step 5 - Therefore, the perimeter of an isosceles triangle is greater than the perimeter of the equilateral triangle.
For more information, refer to the link given below:
https://brainly.com/question/19987277
