Question 150661
1.write true or false. multiplying each number of a Pythagorean  triple be a nonzero whole number yields another Pythagorean triple?


true.
----------------------------------------------------------------------------

2. The longest side of a triangle is 13 centimeters. another side is 11 centimeters. if the triangle is obtuse. right an inequality for the range of values of the third side?


for a right triangle:
{{{a^2+b^2=c^2}}}
{{{11^2+b^2=13^2}}}
{{{121+b^2=169}}}
{{{b^2=48}}}
{{{b=4sqrt(3)}}}


for an obtuse triangle:
{{{a^2+b^2<c^2}}}
{{{11^2+b^2<13^2}}}
{{{121+b^2<169}}}
{{{b^2<48}}}
{{{b<4sqrt(3)}}}


If it is obtuse, b definitely has to be less than 4sqrt3. 


{{{c<a+b}}}
{{{13<11+b}}}
{{{2<b}}}

b also must be more than 2, so that a+b>c and b+c>a.  So,


Answer:
{{{2<b<4sqrt(3)}}}