Question

If each side of a triangle is doubled then find the % increase in area using Heron’s formula. Please give a step-by-step explanation.

Answer 1

Step-by-step explanation:

The area of a triangle with sides a, b and c and semiperimeter (s) = (a+b+c)/2 , by the Heron’s formula is :-

A = √(s) x (s-a) x (s-b) x (s-c)

If all sides become double, the new semiperimeter (s1)=> 2a+2b+2c/2 also becomes double!

Thus, New area (A1) = √ 2s x (2s - 2a) x (2s-2b) x (2s - 2c) = 4 x √(s) x (s-a) x (s-b) x (s-c) = 4 x initial area = 4A.

Thus, change in area => (A1-A)/A x 100 = (4A-A)/A x 100 = 3A/Ax 100 = 300%.

Hope this helps! :)

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