Question 432766
Let's x cm the base of isosceles triangle, Since its perimeter is 36cm, one from the equal sides will be:

{{{(36-x)/2}}}cm  If we draw the altitude on the base, this altitude bisect the 

base. Applying the Pythagorean theorem we can find the base.

{{{(36-x)^2/4-x^2/4=12^2}}},solve the equation,

{{{(1296-72x+x^2-x^2)/4=144}}},multiply by 4 and simplify the equation,

{{{-72x=-720}}}

{{{x=10}}}. As you know the area of triangle is given by the formula:

{{{A=(1/2)*(b*h)}}}, substitute h=12 cm and b=10 cm

{{{A=(1/2)*(10*12)=60cm^2}}}

The area of triangle is 60 cm^2.