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find the percentage increase in the area of a triangle if its each side is doubled

find the percentage increase in the area of a triangle if its each side is doubled

Grade:10

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
Please find the answer to your question below
Heron's formula states for a triangle with sides of lengths a,b,c
A = \sqrt{[s*(s-a)*(s-b)*(s-c)] }
where s = (a+b+c)/2
If you double the sides A1 =\sqrt{[2s*(2s-2a)*(2s-2b)*(2s-2c)] }
= 4*\sqrt{[s*(s-a)*(s-b)*(s-c)]} = 4*A
The percentage increase in area is 4*A-A = 3*A so the answer is 300%

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