Question 330992
Try this:
Let x be the length of the shorter leg and x+2 be the length of the other leg.
Applying the Pythagorean theorem, we get:
{{{32^2 = x^2+(x+2)^2}}} Simplify.
{{{1024 = 2x^2+4x+4}}} Subtract 1024 from both sides.
{{{2x^2+4x-1020 = 0}}} Divide both sides by 2 to simplify a bit.
{{{x^2+2x-510 = 0}}} Solve this by the quadratic formula:{{{x = (-b+-sqrt(b^2-4ac))/2a}}} where: a = 1, b = 2, and c = -510
{{{x = (-2+-sqrt(2^2-4(1)(-510)))/2(1)}}}
You can work this out on your calculator and you should get:
{{{x = -23.605}}} and {{{x = 21.605}}} Discard the negative solution, and your answer is:
{{{x = 21.61}}}Rounded to the nearest hundredth.