anonymous one year ago http://media.education2020.com/evresources/2004-04-01-02-00_files/i0130000.jpg Find the unknown side length, x. Write your answer in simplest radical form

1. mathstudent55

|dw:1440193477028:dw|

2. mathstudent55

We are looking for x.

3. mathstudent55

What do the circled marks mean? |dw:1440193557796:dw|

4. anonymous

@mathstudent55 , the circled marks are called hash marks and lines with the same number of hash marks indicate that these sides are the same length. It saves cluttering up sketches with dimensions. For example, a rectangle might look like |dw:1440193790343:dw|

5. mathstudent55

I believe I knew that. I was asking the poster to see if he/she knew it, so we could work on the problem.

6. anonymous

Yeah I knew what they mean but I figured it out I just asked my E2020 teacher for help even though he didn't get it either. Thank you for you help though

7. mathstudent55

Ok. We know those marks mean the two segments are congruent. That means we can now add this to the|dw:1440194145894:dw| drawing:

8. mathstudent55

Now just look at the triangle at the right. |dw:1440194177047:dw|

9. mathstudent55

What kind of triangle is it?

10. mathstudent55

Sorry, gtg. Here is the rest of the solution. This triangle is a right triangle. We know that because the figure shows a right angle. We can use the Pythagorean theorem. $$a^2 + b^2 = c^2$$ |dw:1440194360342:dw|

11. mathstudent55

Using the formula above for our triangle, we get: $$3^2 + 6^2 = x^2$$ $$9 + 36 = x^2$$ $$45 = x^2$$ $$x^2 = 45$$ $$x = \sqrt {45}$$ Now we need simplest radical form. We factor 45 into 2 factors, one being the largest perfect square factor we can find. $$x = \sqrt {9 \times 5}$$ $$x = 3 \sqrt 5$$

12. mathstudent55

Sorry, but gtg. If you have questions, just ask them.

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