Question

An equilateral triangle has an altitude of 7cm. Which of the following have a proportional relationship to the altitude? Select all that apply.

A. Perimeter
B. Sides
C. Angles
D. Area
E. Vertices

Answer 1

A. Perimeter

B. Sides

D. Area

Explanation:

Suppose a triangle ABC has sides each of length a

formula:

The altitude of the triangle h equal to :

`h=(√(3))/(2) a`

________

Perimeter:

Let’s P be the perimeter of the triangle ABC then P = 3a

`(P)/(h)=(3 a)/((√(3))/(2) a)=(3)/((√(3))/(2))=2 (3)/(√(3))=2 √(3)`

P/h is a constant then The perimeter has a proportional relationship to the altitude

______

Sides :

`(h)/(a)=((√(3))/(2) a)/(a)=(√(3))/(2)`

h/a is a constant then The side has a proportional relationship to the altitude

______

Area :

Let A be the area of the triangle

`(A)/(h)=(a * h)/(h)=a`

A/h is a constant then The area has a proportional relationship to the altitude

_____

Angles :

The measure Of each angle of an equilateral triangle is always equal to 60°

60/h is not a constant then there is no proportional relationship

______

Vertices:

The vertices are points and not numbers so there is no proportional relationship.