Question

In acute triangle ABC, segment AD is an altitude, the measure of angle ADC = 2x2+40, BD=3x+8, and DC=4x+4. Based on this information, explain whether or not triangle ABC is an equilateral triangle. Make sure to support your answer.

Answer 1

angle ADC is equal to 90 degreees since AD is an altitude

Answer 2

Yeah, I was going to fix it

Answer 3

2x^2 + 40 = 90

2x^2 = 50

x^2 = 25

x = 5

Answer 4

angle ADC is a right angle so 2x^2 +40 = 90 and x = 5. If the triangle is equilateral, then BD = CD or 3x+8 = 4x+4. However x is 5 and 2(5)+8 does not equal 4(5)+4. So the triangle could not be equilateral.

Answer 5

Why does BD have to equal CD?

Answer 6

It isn't. I made that assumption.

Answer 7

mertsj is saying that if BD = CD then the triangle would be equilateral. However, BD does not equal CD so it can't be equilateral.

Answer 8

In an equilateral triangle, Colly, the altitude bisects the side. So if the triangle were equilateral, BD would have to equal CD. In your triangle, BD does not equal CD so the triangle is not equilateral.