<p><a href="http://i28.tinypic.com/35mpfyc.png%5B/url%5D">http://i28.tinypic.com/35mpfyc.png</a>
The answer is A</p>
<p>How would you solve this? I'm not sure how to figure out the 3rd leg knowing only h and m... I know you have to use the Pythagorean theorem, but is there an easier/quicker way to solve it as well?</p>
<p>The best way to relate e, m, and h is a right triangle where e is the hypotenuse and h is one of the legs. But how do we get the 3rd side?</p>
<p>The 3rd side is half of a diagonal of a square with side m. Since the full diagonal = sqrt 2 * m (remember, the diagonal of a square divides the square into two 45-45-90 right triangles), half of the diagonal is (sqrt 2 * m)/2.</p>
<p>We now have our three sides and using the Pythagorean theorem
h^2 + [(sqrt 2 * m)/2]^2 = e^2
h^2 + 2m^2/4 = e^2</p>
<p>e = m so…</p>
<p>h^2 + m^2/2 = m^2
h^2 = m^2/2
h = sqrt (m^2/2)
= (sqrt m^2)/(sqrt 2)
= m/(sqrt 2)</p>
