Question

What is the length, in units, of BD?

5 radical 6

5

6 radical 5

9

Answer 1

Use the proportion method.

Answer 2

okay can you explain plz

Answer 3

\[{x \over 12}={15 \over x}\]
Cross multiply.

Answer 4

Do you know how to use the proportion method?

Answer 5

kinda not well

Answer 6

Do you see it now?

Answer 7

yeah so what would be the answer

Answer 8

it's basically two, congruent right angle triangles in one bigger right angle triangle.

Answer 9

\[{x \over 12}\times {15 \over x}\]

Answer 10

can you solve for x? Or do you still need help?

Answer 11

can you show me

Answer 12

To cross multiply, you need to multiply across. In this case, it would be
\[x \times x=15 \times 12\]

Answer 13

Then, find for x.

Answer 14

is 180

Answer 15

\[x^2=180\]
\[x=\sqrt{180}\]

Answer 16

correct.

Answer 17

yeah if you 108 by 2 you 90 and again 42

Answer 18

dived 180*

Answer 19

now, what are the factors of 180 so it can be simplified even further? (one perfect square multiply by another number=180)

Answer 20

90 is not a perfect square. Perhaps you can try again?

Answer 21

42?

Answer 22

Here's an example. Let's say you want to find the factors of 98 so that you can simplify \[\sqrt{98}\] , it would be \[\sqrt{49 \times 2}\]

Answer 23

49 is a perfect square because 7 x 7 = 49

Answer 24

42 is not a perfect square.

Answer 25

yeah okay

Answer 26

here I'll give you a hint... one number is 5

Answer 27

what's the other number that you can multiply by 5 to get 180?

Answer 28

so it answer is 5 radical of 6?

Answer 29

\[{\sqrt{5 \times ?}} = \sqrt{180}\]

Answer 30

not so fast.

Answer 31

I would really like to help you understand a little so next time you will be better at answering questions like this. Please bear with me. We're really close.

Answer 32

okay

Answer 33

what is... \[{180 \over 5} =?\]

Answer 34

36

Answer 35

Correct! Is 36 a perfect square?

Answer 36

yes it is

Answer 37

Ok. Now, you have your equation.

\[\sqrt{5 \times 36}\]
\[\sqrt{5} \times \sqrt{36}\]

Answer 38

what is the square root of 36?

Answer 39

sqaure root of 36 is 6

Answer 40

Right! :)

So now, we have...

\[6 \sqrt5\]

Answer 41

i think I found my answer it is 6 with a radical of 5

Answer 42

Yup! :)

Answer 43

Good job. Thank you for hanging in there.