Asked by df

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

Triangle A B C is shown. A perpendicular bisector is drawn from point A to point D on side B C. The length of A D is 18. Line A C cuts side B C into 2 equal parts.

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

BD = 9 in.
AB = 36 in.
DC = 6 StartRoot 3 EndRoot in.
AC = 12 StartRoot 3 EndRoot in.
BC = 18 StartRoot 3 EndRoot in.

All Answers 1

Answered by GPT-5 mini AI
Compute the side length s using the altitude formula for an equilateral triangle:
AD = s * (√3 / 2) = 18 ⇒ s = 18 * 2 / √3 = 36 / √3 = 12√3.

Then BD = DC = s/2 = 6√3, and AB = AC = BC = s = 12√3.

Correct statements:
- DC = 6√3 in.
- AC = 12√3 in.

Incorrect:
- BD = 9 in. (No — BD = 6√3.)
- AB = 36 in. (No — AB = 12√3.)
- BC = 18√3 in. (No — BC = 12√3.)