Anna says that the length of diagonal SQ is two times the length of diagonal OM.

Is Anna correct? Justify your answer and show all your work. Your work should state the theorem you used to find the lengths of the diagonals.

Question

Anna says that the length of diagonal SQ is two times the length of diagonal OM.

Is Anna correct? Justify your answer and show all your work. Your work should state the theorem you used to find the lengths of the diagonals.

kpop4life123 · Answer

attachment

anonymous · Answer

Do you have an attempt at the solution yet, or are you completely stuck?

kpop4life123 · Answer

no i dont

anonymous · Answer

Alright, no problem.

Let's break this down. We want to know if the diagonal of the rectangle is twice the diagonal of the square. Well, we can find the diagonals by splitting the square and rectangle into triangles.

|dw:1446065423933:dw|

How can we find those missing lengths (hypotenuse)?

kpop4life123 · Answer

do we divide?

anonymous · Answer

Are you familiar with Pythagorean Theorem?

kpop4life123 · Answer

no sorry

anonymous · Answer

Well, I'm assuming that you should, because that is the theorem that they are referring to to find the lengths of the diagonals. But in any case:

`Pythagorean Theorem`:
$\large a^2+b^2=c^2$

where a and b are the side lengths of the right triangle, and c is the hypotenuse of the triangle.

Want want to solve for the hypotenuse (c) of the triangles. In order to do such, we must take the square root of $a^2+b^2$ to isolate the exponent of c.

Therefore, we get:
$\large c= \sqrt{a^2+b^2}$

|dw:1446066194480:dw|

We must use this equation for both triangles and solve for c

anonymous · Answer

That is an equation that you will want to have memorized.

puppylover784 · Answer

CShrix

anonymous · Answer

@Kpop4life123 Does this make sense?

kpop4life123 · Answer

oh ok thanks ill try to memorize it

anonymous · Answer

Sounds good!

Once you find c from both triangles, you need to compare them. Anna says that the diagonal from the rectangle is twice is long as the diagonal from the square. You need to compare both c's and see if this is true!

Let me know if you get stuck again

leenathan · Answer

$$12^2 + 6^2 = SQ^2\144 + 36 = SQ^2\SQ^2 = 180\\SQ= \sqrt{180}$$

leenathan · Answer

^thats SQ

leenathan · Answer

$$6^2 + 6^2 = OM^2\36 + 36 = OM^2\OM^2 = 72 \\OM = \sqrt{72}=OM$$

leenathan · Answer

$$\sqrt{180} =13.416\ 2\times \sqrt{72}= 16.971\\So, \sqrt{180} \neq 2\sqrt{72}$$

leenathan · Answer

So, Sam is wrong. The length of diagonal SQ is NOT two times the length of diagonal OM.