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aaaa aaaa Grade: 9

If each side of a triangle is tripled find change in% in its area.explain it with full steps

7 years ago

Answers : (1)

Priyansh Bajaj AskiitiansExpert-IITD
30 Points

Solution:- Let, the initial sides of triangle be 'a', 'b', and 'c'. Then, semi-perimeter of triangle will be-

s = (a+b+c)/2 and Area of triangle (A) = √s(s-a)(s-b)(s-c).

Now, if each side is tripled. Then, new sides will be 3a, 3b, and 3c. And, semi-perimeter of triangle will be- s'' = (3a+3b+3c)/2  = 3s

and, New area of triangle (A'') = √s''(s''-3a)(s''-3b)(s''-3c) = √3s(3s-3a)(3s-3b)(3s-3c)

                                    A'' = 9 √s(s-a)(s-b)(s-c) = 9A

% change in Area = [(A'' - A)/A] x 100 %

                         = [(9A- A)/A] x 100 % = 800% [ANS]

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Priyansh Bajaj

7 years ago
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