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9 grade maths> find the percentage increase in the area ...

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

Rahul Jiji George , 11 Years ago

Grade 10

1 Answers

SHAIK AASIF AHAMED

Last Activity: 11 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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