Question

if each side of a triangle is doubled then how many times the area of triangle increase ​

Answer 1

Answer:

Step-by-step explanation:

let the sides of the triangle be a, b and c

so, original s=(a+b+c)/2

new s=(2a+2b+2c)/2

          =2(a+b+c)/2

          =a+b+c

let original s be x

so new s=2x

now,

original area=√x(x-a)(x-b)(x-c)

again,

new area=√2x(2x-2a)(2x-2b)(2x-2c)

               =√2x*2(x-a)*2(x-b)*2(x-c)

                =4√x(x-a)(x-b)(x-c)

but we know that

√x(x-a)(x-b)(x-c)=original area

so, new area is 4 times the original area

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Answer 2

lets a , b an c are 3 sides of triangle

so area of triangle by Herons formula

$area \: = \sqrt{(s)(s - a)(s - b)(s - c)} \\ where \: s \: = \frac{a + b + c}{2}$

so new sides are 2a, 2b and 2c.

so new s' = (2a+2b+2c)/2 = 2*(a+b+c)/2

= 2* s

so new area is

new area = root ((s')(s'-2a)(s'-2b)(s'-2c))

= root ((2s)(2s-2a)(2s-2b)(2s-2c))

= root ((2*2*2*2)(s)(s-a)(s-b)(s-c))

= root(16) * (old area)

= 4 * (old area)

so new area woild be 4 times of old one