Question 590102
 AB has a scale of 2. BC has a scale of 4 and CA has a scale of 5.
<pre>
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 = {{{sqrt(s*(s-a)*(s-b)*(s-c))}}}

a = AB = 2k, b = BC = 4k, c = CA = 5k

s = semiperimeter = {{{(a+b+c)/2}}} = {{{(AB+BC+CA)/2}}} = {{{(2k+4k+5k)/2}}} = {{{(11k)/2}}}

s-a = {{{(11k)/2}}}-2k = {{{(11k)/2}}}-{{{(4k)/2}}} ={{{7k/2}}}

s-b = {{{(11k)/2}}}-4k = {{{(11k)/2}}}-{{{(8k)/2}}} ={{{3k/2}}}

s-c = {{{(11k)/2}}}-5k = {{{(11k)/2}}}-{{{(10k)/2}}} ={{{k/2}}}

Substituting in

Area = {{{sqrt(s*(s-a)(s-b)(s-c))}}}

450 = {{{sqrt(expr(11k/2)*expr(7k/2)*expr(3k/2)*expr(k/2))}}}

450 = {{{sqrt(231k^4/16)}}}

Square both sides:

202500 = {{{231k^4/16}}}

Multiply both sides by 16

3240000 = 231k<sup>4</sup>

Divide both sides by 231

{{{3240000/231}}} = k<sup>4</sup>

Take fourth roots of both sides:

{{{root(4,3240000/231)}}} = 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</pre>