Question

Which of the following represents the relationship in the image.

A) The perimeter, P, is equal to the length of a side of one triangle multiplied by the number of triangles in the figure, n, plus two times the length of the base. The equation for the perimeter is P = 6n + 10.

B) The perimeter, P, is equal to the length of the base of one triangle multiplied by the number of triangles in the figure n, plus the length of another side. The equation for the perimeter is P = 5n + 6.

C) The perimeter, P, is equal to the length of the base of one triangle multiplied by the number of triangles in the figure n, plus the length of the base. The equation for the perimeter is P = 6n + 5.

D) The perimeter, P, is equal to the length of the base of one triangle multiplied by the number of triangles in the figure n, plus two times the length of another side. The equation of the perimeter is P = 5n + 12.

Answer 1

D

Explanation:

You can simply try out all the options. The simplest example in the image is the first one, whose perimeter(P)=17 units. The number of triangles(n) is 1. The first choice, A, says P = 6n + 10. We can plug the numbers in to get 17 = 6(1) + 10=16. 17≠16, so Option A is false.

The second choice, B, says P = 5n + 6. You can plug it in to get 17 = 5(1) + 6=11. 17≠11, so Option B is false.

The third choice, C, says P = 6n + 5. However, the explanation says P is equal to the length of the base on one triangle multiplied by the number of triangles in the figure n, so I'm guessing the equation is supposed to be P = 5n + 5. You can plug the numbers in again to get 17 = 5(1) + 5=10. 17≠10, so Option C is also false.

The fourth choice, D, says P = 5n + 12. You can plug the numbers in, getting 17 = 5(1) + 12=17. 17=17, so Option D is the only true option.