find the value of x in a triangle? one leg is 16 and value inside the triangle is 2x-6

Question

mathstudent55 · Answer

The value inside the triangle corresponds to what? Is there a figure?

anonymous · Answer

yes scanning it in now and will attach in a few

anonymous · Answer

attachment

anonymous · Answer

how do you do these problems?  I dont understand them.

mathstudent55 · Answer

In a triangle, the segment that connects the midpoints of two sides is parallel to the third side and half the length of the third side.

mathstudent55 · Answer

The statement above allows you to write an equation with 16 and 2x - 6. Then solve for x.

anonymous · Answer

so would the equation be 2x-6=16

anonymous · Answer

so then 2x=10 so x=5

anonymous · Answer

did I do the problem correctly?

anonymous · Answer

I also have another problem I do not understand.  What is the range of possible values for x?

mathstudent55 · Answer

No, your equation is not correct.
Read the statement above again.
The segment that connects the midpoints does not have the same length as the third side. It's half of the third side. The third side measures 16. The segment connecting the midpoints measures 2x - 6. That is the same as half of the side that measures 16.

anonymous · Answer

so 2x=22 so x =11

mathstudent55 · Answer

For the second problem, notice that sides TR and BD are congruent, and sides TS and DC are also congruent. Also, RS = 16 and BC = 13. That means that RS > BC. That means that m<D must be less than the m<D. Since the measure of angle T is 42, and angle D must be less than 42, then the inquality you get is 0 < 6x - 30 < 42. In other words, the measure of angle D is between 0 and 42.

mathstudent55 · Answer

2x = 22 is not correct.
Which equation did you get from the given information of 2x - 6 and 16?
Also, according to the statement I gave you above, what must be the length of the segment that connects the midpoints?

anonymous · Answer

is the equation 2x-6=16
                       2x+6=16+6
                        2x=22
                          x=11

anonymous · Answer

i dont understand what you mean?  could you show me

mathstudent55 · Answer

|dw:1368039523766:dw|

mathstudent55 · Answer

Look at the figure above. What does AB measure?

anonymous · Answer

16

mathstudent55 · Answer

good
What does CD measure in terms of x?

anonymous · Answer

2x-6

mathstudent55 · Answer

good.

mathstudent55 · Answer

Read this statement carefully:
In a triangle, the segment (CD) that connects the midpoints of two sides is parallel to the third side and half the length of the third side (AB).
What is this statement telling about the length of CD compared to the length of AB?

anonymous · Answer

it is 1/2

mathstudent55 · Answer

Right. SO if AB is 16, what is CD?

anonymous · Answer

8

mathstudent55 · Answer

But CD is 2x - 6, right? Now you can set up your equation.

anonymous · Answer

2*8-6

mathstudent55 · Answer

No. 
CD = 8 and CD = 2x - 6, so
2x - 6 = 8

mathstudent55 · Answer

That's the equation. Now solve it for x.

anonymous · Answer

thank you I told you I didnt get what I was supposed to do

mathstudent55 · Answer

When you wrote the equation before as 2x - 6 = 16, that means that the segment also measures 16, which is not true.The segment does not measure the same as the third side, it measure half of the third side.

mathstudent55 · Answer

Now you can solve the equation for x and get an answer.

anonymous · Answer

Thanks again you made me understand it

mathstudent55 · Answer

Remember is't 2x - 6 = 8 that you need to solve.

mathstudent55 · Answer

Great. You're welcome.

anonymous · Answer

x=7

mathstudent55 · Answer

Correct!

mathstudent55 · Answer

Now you can check. 2x - 6, with 7 in for x is 2(7) - 6 = 14 - 6 = 8. Since 8 is half of the side of 16, x = 7 is correct.