Question

If each side of a triangle is doubled then find than how many times its area is double

Answer 1

Answer:

Area is 4 times  (4 = 2×2 means two time double)

Step-by-step explanation:

Let Say Δ ABC

AB = a  

BC = b

CA = c

area of Δ ABC = √{s(s-a)(s-b)(s-c)    - Eq 1

where s = (a + b + c )/2      - Eq2

Let Say Δ DEF

DE = 2a

EF = 2b

DF = 2c

S = (2a + 2b + 2c)/2

S = 2(a+b+c)/2

S = 2s     putting value of s deom Eq 2

Area of ΔDEF = √{S(S-2a)(S-2b)(S-2C)

putting value of S = 2s

= √{2s(2s-2a)(2s-2b)(2s-2c)

= √{2s×2(s-a)×2×(s-b)×2×(s-c)

= 4 √{s(s-a)(s-b)(s-c)

= 4 (area of Δ ABC)    from Eq 1

Area of ΔDEF = 4 (area of Δ ABC)

Hence Area is 4 times  (4 = 2×2 means two time double)