11 with method

​Q11. Ratio of the area of a triangle to the product of its sides is _________ times the reciprocal of its circum -radius.
 

Dear Student ,
 
Please find below the solution to the asked query :



Area of triangle=12×base×height=12×BC×ADProduct of sides of triangle=AB×BC×ACRatio of the area of triangle to the product of its side=12×BC×ADAB×BC×ACRatio of the area of triangle to the product of its side=AD2×AB×AC   ... 1Circumradius=Product of two sidesdouble of altitude from common vertex of these sidesCircumradius =AB×AC2×ADReciprocal of circumradius=2×ADAB×ACReciprocal of circumradius=2×2×AD2×AB×ACReciprocal of circumradius=4 Ratio of the area of triangle to the product of its side          Using eqn i 14 Reciprocal of circumradius=Ratio of the area of triangle to the product of its sideThus,answer is 14 times .
 
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