Question 36379
The sides of the triangle are 6,7,and x. What is the largest value that could be the area of such a triangle?
HOPE YOU KNOW ELEMENTARY TRIGNOMMETRY.THEN IT IS VERY EASY.OTHERWISE ,PLEASE INFORM AND I SHALL SHOW YOUB ANOTHER METHOD 
AREA OF TRIANGLE =(1/2)*BASE*ALTITUDE=0.5*b*h=0.5*b*c*SIN(A)=0.5*6*7*SIN(A)
=21SIN(A).....WE KNOW THAT MAXIMUM VALUE OF SIN(A)=1 WHEN A=90 DEGREES 
HENCE MAXIMUM AREA =21*1=21 WHEN IT IS RIGHT ANGLED TRIANGLE WITH LEGS EQUAL TO 6 AND 7.