Question

Triangle ABC is an equilateral triangle. Segment AD measures 18 inches.


Which statements about the diagram are correct? Check all that apply.


A )BD = 9 in. B) AB = 36 in. C) DC = 6 squared root of 3 in.

D) AC = 12 squared root of 3 in. E) BC = 18 squared root of 3 in.

The answer is C and D

Answer 1

Answer:

C and D

Step-by-step explanation:

Answer 2

Finding the sides of the equilateral triangle, it is found that the correct options are:

C. $DC = 6\sqrt{3}$

D. $AC = 12\sqrt{3}$

In an equilateral triangle, all sides have the same measure.

In this question, it means that:

• $AB = BC = AC = 18$
• Side BC is bisected into two equal parts, thus $BD = DC = \frac{x}{18}$

Sides BD and DC are both a side of a right triangle, in which the other side is 18 and the hypotenuse is x, thus, applying the Pythagorean Theorem:

$(\frac{x}{2})^2 + 18^2 = x^2$

$\frac{x^2}{4} + 324 = x^2$

$\frac{3x^2}{4} = 324$

$x^2 = \frac{324 \times 4}{3}$

$x^2 = 432$

$x = \sqrt{243}$

Using prime factors:

$x = \sqrt{2^4 \times 3^3}$

$x = 2^2 \times 3\sqrt{3}$

$x = 12\sqrt{3}$

Thus, the lengths of the segments are:

$AC = AB = BC = 12\sqrt{3}$

Which means that option D is correct.

For the bisection:

$BD = DC = \frac{x}{2} = 6\sqrt{3}$

Which means that option C is also correct.

A similar problem is given at https://brainly.com/question/5502236