Question 611167
The sides of the 2 triangles are proportional
Suppose you have a 3-4-5 right triangle
The bigger 3-4-5 triangle which is similar has
sides 3k-4k-5k where k is a positive number
greater than 1.
The pythagorean formula for the larger triangle is:
{{{ (3k)^2 + (4k)^2 = (5k)^2 }}}
{{{ k^2*(3^2) + k^2*(4^2) = k^2*(5^2) }}}
{{{ k^2*( 3^2 + 4^2 ) = k^2*(5^2)  }}}
So, the Pythagorean formula gets multiplied by
{{{k^2}}} when the larger triangle's sides are
{{{k}}} times larger.