Sir/Ma`am
By how much percent the area of a triangle increases if its side are tripled ??

Asked by SIDDHARTH SHARMA | 10th Sep, 2014, 03:16: PM

Expert Answer:

L e t space apostrophe a apostrophe comma apostrophe b apostrophe comma space apostrophe c apostrophe space b e space t h e space s i d e s space o f space a space t r i a n g l e. T h u s space A subscript o r i g i n a l end subscript equals square root of s subscript 1 open parentheses s subscript 1 minus a close parentheses open parentheses s subscript 1 minus b close parentheses open parentheses s subscript 1 minus c close parentheses end root comma space w h e r e comma space s subscript 1 equals fraction numerator a plus b plus c over denominator 2 end fraction N e w space s i d e s space o f space t h e space t r i a n g l e equals 3 a comma space 3 b comma space 3 c T h u s comma space b y space H e r o n apostrophe s space f o r m u l a comma A subscript n e w end subscript equals square root of s subscript 2 open parentheses s subscript 2 minus a close parentheses open parentheses s subscript 2 minus b close parentheses open parentheses s subscript 2 minus c close parentheses end root comma space w h e r e space s subscript 2 equals fraction numerator 3 a plus 3 b plus 3 c over denominator 2 end fraction equals 3 open parentheses fraction numerator a plus b plus c over denominator 2 end fraction close parentheses equals 3 s subscript 1 space space space space space space space space equals square root of 3 s subscript 1 open parentheses 3 s subscript 1 minus 3 a close parentheses open parentheses 3 s subscript 1 minus 3 b close parentheses open parentheses 3 s subscript 1 minus 3 c close parentheses end root space space space space space space space space equals square root of 3 to the power of 4 s subscript 1 open parentheses s subscript 1 minus a close parentheses open parentheses s subscript 1 minus b close parentheses open parentheses s subscript 1 minus c close parentheses end root space space space space space space space space equals 3 squared square root of s subscript 1 open parentheses s subscript 1 minus a close parentheses open parentheses s subscript 1 minus b close parentheses open parentheses s subscript 1 minus c close parentheses end root space space space space space space space space equals 3 squared A subscript o r i g i n a l end subscript T h e space p e r c e n t a g e space i n c r e a s e space i n space t h e space a r e a equals fraction numerator A subscript n e w end subscript minus A subscript o r i g i n a l end subscript over denominator A subscript o r i g i n a l end subscript end fraction cross times 100 % space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 9 A subscript o r i g i n a l end subscript minus A subscript o r i g i n a l end subscript over denominator A subscript o r i g i n a l end subscript end fraction cross times 100 % equals 800 %

Answered by Dharma Teja | 10th Sep, 2014, 04:36: PM

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