Question

What is the length of leg s of the triangle below?
(Picture below & Medals rewarded.)

Answer 1

hypotenuse= √2 times leg

Answer 2

Pythagorean theorem applies here because this is a right triangle. We know the hypotenuse, \(c = \sqrt{72}\). We also know that one of the legs \(a = 6\). We can find the other leg with Pythagorean theorem:

\[a^2+b^2=c^2\]\[6^2+b^2 = (\sqrt{72})^2\]\[36 + b^2 = 72\]\[b^2=36\]\[b=6\]
(\(b\) is labeled S in your diagram, btw)

Another way to find the side is to notice that this is an isosceles triangle, with the unknown side being one of the pair of sides of equal length. We know the length of the other one in the pair, so we can determine that \(s = 6\) by simply looking at the triangle.

Answer 3

@notgoodatmathguy12's suggestion is also true, but only applies to isosceles triangles, and if you've figured out that it is an isosceles triangle, why not just copy the length of the other side instead of dividing the hypotenuse by \(\sqrt{2}\)?