Question 65188
11. Find the length of the hypotenuse if the two legs are 20cm and 15cm.
Remember that in a right triangle, the lengths of the sides are in proprtion to: 3, 4, and 5, and the hypotenuse is always the longest side.

So:
15 = 3*5
20 = 4*5
x = 5*5 = 25

The hypotenuse is 25cm.

6. Simplify:
{{{2sqrt(12)/4sqrt(27)}}} Cancel 2 in the top and bottom.
{{{sqrt(12)/2sqrt(27)}}} Simplify the square roots.
{{{sqrt(3*4)/2sqrt(3*9)}}}
{{{2sqrt(3)/3*2sqrt(3)}}} Cancel where appropriate.
{{{1/3}}}

10. The distance between two points, (x1, y1) and (x2, y2) is given by:
{{{d = sqrt((x2-x1)^2 + (y2-y1)^2)}}} Applying this to your two points:(4, 0) and (-9, 0)
{{{d = sqrt((-9-4)^2 + (0-0)^2)}}}
{{{d = sqrt((-13)^2)}}}
{{{d = sqrt(169)}}}
{{{d = 13}}}