Question 125342
Use the Pythagorean theorem to find the height of a right triangle if the hypotenuse is 20 and the base is 16.
{{{c^2 = a^2+b^2}}} Substitute c = 20, a = 16, and b = h
{{{20^2 = 16^2+h^2}}} 
{{{400 = 256 + h^2}}} Subtract 256 from both sides.
{{{144 = h^2}}} Take the square root of both sides.
{{{12 = h}}} We discard the negative answer because the height of a triangle is positive.
So the triangle has side: 20, 16, and 12
a) The perimeter is:
{{{P = 20+16+12}}}
{{{P = 48}}}
b) The area is:
{{{A = (1/2)bh}}} Substitute b = 16 and h = 12.
{{{A = (1/2)(16)(12)}}}
{{{A = 96}}}sq. units.