triangles

Maxp070704 said:
Easy question. Solve for x. If BD is a median, AD=AC so 6x + 10 = 2x + 12. X = 1/2. So AC is equal to 13 x 2 = 26
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Careful!

Although your work is correct - it is sloppy.

You have x and X as the same variable - then x as the sign of multiplication. Disaster waiting to happen!!
 
rachelmaddie said:
Is that correct?
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rachelmaddie said:
6x + 10 = 2x + 12
6x - 2x = 12 - 10
4x = 2
x = 2/4 = 1/2
AD + DC = AC
6x + 10 + 2x + 12 = AC
8x + 22 = AC
8(1/2) + 22 = AC
4 + 22 = AC
AC = 26
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For this, I don't understand why you need to add the 8x + 22 = AC, if you know AD is 13 from the equation, just times it by 2 since AD = DC and AD + DC = AC so 2AD = AC so the answer is 13. Hope this helps.
 
Use your equation, 6x + 10, if x = 1/2. So 6 * 1/2 + 10 = 13. times that by 2. I think you didn't clarify what x is.
 
Maxp070704 said:
Use your equation, 6x + 10, if x = 1/2. So 6 * 1/2 + 10 = 13. times that by 2. I think you didn't clarify what x is.
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x was given (in OP) as an unknown variable (without any physical or geometric significance) whose value was calculated to be 1/2.
 
rachelmaddie said:
For #14, is this the angle bisector theorem? I need help with setting up an equation.

View attachment 14801
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The median BD bisects AC into two equal parts, namely AD and CD. So 6x+10 = 2x+12. The AC is twice the length of AD (or CD). If we can find x, then we can find the length of AD (or CD).
But we have 6x+10 = 2x+12 or 4x=2. So 2x=1. CD = 2x+12 = 1 +12 =13. So AC =2*13=26 and I did not use the angle bisector theorem mainly because a median does NOT bisect an angle but rather bisects a line segment.
 
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