Originally Posted by

**MakeANote** Hey there fabxx,

Given that the triangle is a right triangle, side lengths can be found by Pythagoras.

a) 2, 5 and sqrt 29

$\displaystyle \sqrt {2^2 + 5^2} = \sqrt {29}$

a. is possible.

b)2, 5, 7

$\displaystyle \sqrt {2^2 + 5^2} = \sqrt {29} \neq {7}$

b. is not possible.

c)3, 3, and 3sqrt2

$\displaystyle \sqrt {3^2 + 3^2} = \sqrt {18} = \sqrt {9} \ * \sqrt {2} = 3 \sqrt{2}$

c. is possible.

d)3, 4,5

$\displaystyle \sqrt {3^2 + 4^2} = \sqrt {25} = 5$

d. is possible

e)4,5, and sqrt 41

$\displaystyle \sqrt {4^2 + 5^2} = \sqrt {41}$

By Pythagoras, this appears possible, but based on the information on the graph (point above triangle given as (4, 10)), no two side lengths can be greater than (or equal to) 4.

e. is not possible

Trust this helps...

Please show the steps.

Thanks in advance