Question

The pentagon ABCDE has been divided into six isosceles triangles, which all have the same perimeter. The triangle ABC is even equilateral. What is the ratio of the perimeter of the triangle ABC to the perimeter of the pentagon ABCDE?

A) 1:3
B) 4:9
C) 3:7
D) 9:16
E) 5:8​

Answer 1

Unfortunately, none of the answer choices match. A correct ratio would be 1:2.

Explanation:

Let the perimeter of each isosceles triangle be "2x". Since ABC is equilateral, each of its sides is also "2x".

The perimeter of the pentagon is the sum of the perimeters of the triangles, which is 6(2x) = 12x.

Since ABC is equilateral, its perimeter is 6x (since it has three sides of length 2x).

Therefore, the ratio of the perimeter of ABC to the perimeter of ABCDE is (6x)/(12x) = 1/2, simplifying this ratio gives 1:2.

Therefore, the correct answer is not given in the options.