AB has a scale of 2. BC has a scale of 4 and CA has a scale of 5.
Let k be the constant that you have to multiply 2 by to get the length of AB,
4 by to get the lebnth of BC, and 5 by to get the kength of CA
AB = 2k, BC = 4k, CA = 5k
Now we use Heron's formula for the area:
Area =
a = AB = 2k, b = BC = 4k, c = CA = 5k
s = semiperimeter = = = =
s-a = -2k = - =
s-b = -4k = - =
s-c = -5k = - =
Substituting in
Area =
450 =
450 =
Square both sides:
202500 =
Multiply both sides by 16
3240000 = 231k4
Divide both sides by 231
= k4
Take fourth roots of both sides:
= k
10.88261481 = k
AB = 2k = 2(10.88261481) = 21.76522962
BC = 4k = 4(10.88261481) = 43.53045924
CA = 5k = 5(10.88261481) = 54.41307405
[It's much easier if you are given the perimeter instead of the area]
Edwin