Question

The areas of two similar triangles are 25 and 16. If the perimeter of the first is 15, find the perimeter of the second.

I know the answer is 12, but I do not know how to get there.

Answer 1

according to theorem we know that, ratio of the area of two similar triangle is equal to sq. of ratio of their Coressponding sides;

there is also a theorem that shows that ratio of perimeter of two similar triangle is equal to ratio of their Coressponding sides;

let second perimeter be'x'

from these both theorem

25/16=(15×15) /x^2

x^2=(16×15×15) /25

x^2=16×9

x^2=144

x=12