Grade 109 grade maths

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

Rahul Jiji George

11 Years agoGrade 10

1 Answer

SHAIK AASIF AHAMED

Approved Tutor Answer11 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%