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