Quadrilateral and Pythagorean theorem on right triangles!

[Cake]

Hey Guys,

I don't know how to get the answer to this problem.

I've tried :

6^2 + 8^2 = c^2 (which is 100)

so I get 10 for RT

Now I have UR = 15 which is the hypotenuse
so 15^2 = 225
I also have 10 for RT
so 10^2= 100

doing pythagorean formula
I have 100 + b^2 = 225

b^2 = 5^2
which is 125


The correct answer is 5 radical 5
5√5

lol. I'm so dumb. I thought 125 = 5 when it's obviously 25*5 which is 5√5.
Lol. I spent like 25 minutes on this problem.
Oh well. I'm going to post it anyways. Hope somebody laughs. hahaha

I thought square root of 125 was 5..............
oh man. Long day today and only running on 4 hours of sleep. sigh. I think this has been the biggest brain fart I've had.

 

[stapel]

Yes, the book's answer is correct. I'm glad to see that you were able to find your mistake and correct it. Thank you for showing your work and reasoning so nicely!

 

[Cake]

Yes, the book's answer is correct. I'm glad to see that you were able to find your mistake and correct it. Thank you for showing your work and reasoning so nicely!

Yes, so am I haha. I will always post my work and the methods I have tried :smile:. Have a good day!