Question 224258

A triangle similar to a 3-4-5 triangle would have a ratio that is consistent with a 3-4-5 triangle. In other words, if 1 side of the new triangle is doubled, then the other sides of the new triangle should also be doubled. Furthermore, when the area of the larger of 2 similar triangles is quadrupled, its sides were obviously doubled. 


The only choice that fits these criteria is CHOICE C. As seen, each of its sides was doubled (2*3=6, 2*4=8, 2*5=10) to form a 6-8-10 triangle. 


Now, just to make sure we have the correct choice, we can calculate each area to see if the new and similar 6-8-10 triangle has an area that is 4 times the original 3-4-5 triangle.


Area of 3-4-5 triangle: {{{(1/2)*B*H = (1/2)*4*3 = 6}}} square units


Area of 6-8-10 triangle: {{{(1/2)*B*H = (1/2)*8*6 = 24}}} square units


It is quite obvious that the 6-8-10 similar triangle's area of 24 square units is 4 times the area of the 3-4-5 similar triangle's area of 6 (24 = 4 * 6)


Therefore, the correct answer is CHOICE {{{highlight_green(c)}}}