In similar triangles ABC and DEF, corresponding sides AB and DE equal 15 and 12, respectively. If the perimeter of triangle ABC=40, what is the perimeter of triangle DEF

Answer 1

because of similar triangles, each side of triangle DEF is 12/15 or 4/5 as long as the corresponding sides of ABC
in first
a+b+15 = 40
a+b = 25

in DEF
perimeter = e+d + 12
= (4/5)b + (4/5)a + 12
= (4/5)(b+a) + 12
= (4/5)(25) + 12
= 32

Or
by just "common sense" if each side is 4/5 of the old triangle then the new perimeter is (4/5) of 40 or 32