Question

In the isosceles right triangles ABC and MNP, AB = BC = 12 and MN = NP = 24. Which is the sum of the hypotenuses of these triangles?

16 square root 2
18 square root 2
32 square root 2
36 square root 2
i got the 2cd one..

Answer 1

Using the pythagorean theorem we can get the hypotenuses of the triangles:
\[h_{1} = \sqrt{12^{2}+12^{2}} = \sqrt{2(12)^{2}} = 12\sqrt{2}\]
Likewise the second hypotenuse will be \[24\sqrt{2}\]
adding them gives \[36\sqrt{2}\]

Answer 2

Well, by the Pythagorean Theorem, the hypotenuse of the first triangle is \[\sqrt(12^2 + 12^2) = \sqrt(2*12^2) = 12*\sqrt(2)\]
and the hypotenuse of the second one is \[\sqrt(24^2 + 24^2) = \sqrt(2*24^2) = 24*\sqrt(2)\]
Then the sum of these is (24+12) square roots of 2, or \[36*\sqrt(2)\]

Answer 3

gj joe

Answer 4

thank you :)

Answer 5

Curses, Joe beat me to it!

Answer 6

gj Blacksteel :)

Answer 7

gj blacky!

Answer 8

its not a race! (although sometimes it feels like it is <.<) lol

Answer 9

no no it is a race

Answer 10

lol