Question

An equilateral triangle with side lengths of 8.7 centimeters is shown. An apothem has a length of a and the radius has a length of 5 centimeters. The apothem and radius form a triangle with a base length of b.
Which statements about finding the area of the equilateral triangle are true? Select three options.

The apothem can be found using the Pythagorean theorem.
The apothem can be found using the tangent ratio.
The perimeter of the equilateral triangle is 15 cm.
The length of the apothem is approximately 2.5 cm.
The area of the equilateral triangle is approximately 65 cm2.

Answer 1

Options A,B and D. The correction about the area of the triangle are

• The apothem can be found using the Pythagorean theorem.
• The apothem can be found using the tangent ratio.
• The length of the apothem is approximately 2.5 cm.

How to solve for the length of the Apothem using the Pythagoras theorem

Firstly this is an equilateral triangle

3 of the sides have the length of 8.7cm

b = half of 8.7

= 4.35cm

To get A we have

a² + b² = c²

a² + 4.35² = 5²

When we solve this out we would have

a² = 25 - 18.9225

a ≈ 2.5 cm.

Hence we have proved that the first option is correct.

For B,

In an equilateral triangles, each of the angles = 60 degrees

60/2 = 30 is the angle that is made from the base

using tangent ratios

a / 4.35 = tan 30

then a = 4.35 tan 30

This would also give us an approximate of 2.5

For D

The calculations we have done based on the statements in A and B shows that D is correct as 2.5.

Read more on triangles here:

brainly.com/question/18404158

#SPJ1