Question 389532
if the larger triangle is similar, it's sides will be in the same
ratios as the smaller triangle, namely 4:6:7
The longest side of the larger triangle corresponds to
the longest side of the smaller triangle.
Suppose I call the sides of the larger triangle {{{a}}},{{{b}}}, and {{{21}}}
I can say
(1) {{{4/6 = a/b}}}
(2) {{{6/7 = b/21}}}
In (2), I can solve for {{{b}}}
{{{6 = b/3}}}
{{{b = 18}}}
Now I can plug this into (1)
{{{4/6 = a/18}}}
{{{4 = a/3}}}
{{{a = 12}}}
So, the sides of the larger triangle are {{{12}}},{{{18}}}, and {{{21}}}
Notice this is 3 x {{{4}}}, 3 x {{{6}}}, and 3 x {{{7}}}
The larger triangle is "scaled up" by a factor of 3
The perimeter is {{{12 + 18 + 21 = 51}}}